Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Please note that all times are shown in the time zone of the conference. The current conference time is: 18th Aug 2022, 09:44:58pm CEST

Session Overview
Date: Monday, 27/June/2022
9:30am - 10:45amSC1: Short Courses 1
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
9:30am - 10:30am

Various Collision Models for LBE

Luo, Li-Shi

CSRC, China, People's Republic of

Various Collision Models for LBE

10:45am - 11:00amCoffee Break
11:00am - 12:15pmSC2: Short Courses 2
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
11:00am - 12:00pm

Two approximations of the Euler equations using a non conservative formulation

Abgrall, Rémi

University of Zurich, Switzerland

Two approximations of the Euler equations using a non conservative formulation

12:15pm - 1:45pmLunch
Location: Room MSI 218, Maison des Sciences de l'Ingénieur (MSI), La Rochelle University
1:45pm - 3:00pmSC3: Short Courses 3
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
1:45pm - 2:45pm

Recursive asymptotic analysis for the lattice Boltzmann method

Geier, Martin

TU Braunschweig, Germany

The lattice Boltzmann equation was first proposed as a rule based physical model mimicking the behavior of undistinguishable particles in a gas, rather than a discretization of a partial differential equation. Different asymptotic techniques have since been proposed with the aim of linking the lattice Boltzmann equation to a particular differential equation, to analyze boundary conditions and to improve the accuracy of the method. These techniques include the Chapman Enskog method, the plain Taylor expansion method and the asymptotic expansion in a numerical smallness parameter. Expansions are often applied directly to the distribution functions and moments are obtained through a transformation matrix as known form Multiple Relaxation Time methods. In this lecture we will investigate a matrix free expansion in countable raw moments. Through recursion of the collision operators of different moments this expansion can be reduced to an expansion in the primitive variables and hence leads very naturally to the partial differential equation being solved. The purpose of this method is to make analyzing lattice Boltzmann methods as simple as possible, both in the manual and the computer algebra aided context.

3:00pm - 3:15pmCoffee Break
3:15pm - 4:30pmSC4: Short Courses 4
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
3:15pm - 4:15pm

LBM as a general numerical method: fluid dynamics and beyond

Sagaut, Pierre

Aix-Marseille University, France

LBM as a general numerical method: fluid dynamics and beyond

4:30pm - 5:45pmSC5: Short course 5
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University

Equivalent finite difference schemes for the magic TRT lattice Boltzmann method

Dellar, Paul

University of Oxford, United Kingdom

Equivalent finite difference schemes for the magic TRT lattice Boltzmann method

5:45pm - 7:00pmQ&A for short courses
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Date: Tuesday, 28/June/2022
8:30am - 9:00amWelcome
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Li-Shi Luo, CSRC
9:00am - 9:50amInvited speaker
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Li-Shi Luo, CSRC

Radiative Transfer in Fluids: from Mathematical Analysis to Numerical Simulations

Golse, François

Ecole polytechnique, France

This talk presents a simplified model for radiative transfer in a fluid governed by the Navier-Stokes equations. The fundamental mathematical properties of this simplified model (existence, uniqueness, a priori estimates) will be described in detail. A rather efficient numerical algorithm for computing the solutions of this model - involving the source iteration method for the radiative transfer part of the resulting system is proposed, and its convergence is discussed. Several numerical simulations based on this algorithms will be presented. (Joint work in collaboration with O. Pironneau and C. Bardos)

9:50am - 11:10amAlgorithms and Implementations etc.
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: François Golse, Ecole polytechnique
9:50am - 10:10am

Towards compressible lattice Boltzmann methods for industry-oriented applications

Coreixas, Christophe1,2; Latt, Jonas1; Shan, Xiaowen2

1Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland; 2Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China

Lattice Boltzmann methods (LBMs) are well-established alternative solutions to Navier-Stokes-Fourier (NSF) solvers for the simulation of isothermal and weakly compressible flows past realistic geometries. Nevertheless, fully compressible LBMs have difficulties to compete with NSF solvers due to an increased size of the lattice required to get the correct macroscopic behavior, and/or complexity of the numerical scheme to ensure stable simulations. This is especially true since industry-oriented compressible LB solvers do not benefit from hardware acceleration (e.g., GPUs), unlike a number of academic and commercial solvers based on NSF equations.

In this presentation, we focus on the key requirements for the design of compressible LBMs dedicated to industrial applications. Specifically, we summarize recent research at the University of Geneva, which aims to satisfy a number of requirements for realistic overnight simulations: (1) trade-off between accuracy/robustness/efficiency [1-3], (2) turbulence and wall modeling [4,5], (3) hardware-agnostic and easily maintainable solver [6-9] and (4) adaptive mesh refinement in velocity and geometric space [2,8-10].

[1] Latt, Coreixas, Beny and Parmigiani, Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria, Phil. Trans. R. Soc. A, 2020.

[2] Coreixas and Latt, Compressible lattice Boltzmann methods with adaptive velocity stencils: an interpolation-free formulation, Phys. Fluids, 2020.

[3] Thyagarajan, Coreixas and Latt, Compressible lattice Boltzmann methods based on numerical collision, 18th ICMMES, 2022.

[4] Malaspinas and Sagaut, Advanced large-eddy simulation for lattice Boltzmann methods: The approximate deconvolution model, Phys. Fluids, 2011.

[5] Malaspinas and Sagaut, Wall model for large-eddy simulation based on the lattice Boltzmann method, J. Comput. Phys., 2014.

[6] Latt, Coreixas and Beny, Cross-platform programming model for many-core lattice Boltzmann simulations, PLoS One, 2021.

[7] Latt, Coreixas, Brito and Larkin, Multi-GPU programming with standard parallel C++, NVIDIA's Blog, 2022.

[8] Latt and Coreixas, GPU performance of lattice Boltzmann simulations on non-uniform meshes, SimRace, 2021.

[9] Latt and Coreixas, GPU on non-uniform meshes: a modern implementation approach and detailed decomposition of performance, 18th ICMMES, 2022.

[10] Thorimbert et al., Local mesh refinement sensor for the lattice Boltzmann method, arXiv:1507.06767v3 (under review), 2022.

10:10am - 10:30am

Facing Challenges in Computational Fluid Mechanics with Lattice Boltzmann Methods and High-Performance Computers

Krause, Mathias J.

Lattice Boltzmann Research Group, KIT, Germany

An overall strategy for numerical simulations and optimization of fluid flows is introduced. The integrative approach takes advantage of numerical simulation, high performance computing (HPC) and newly developed mathematical optimization techniques, all based on a mesoscopic model description and on Lattice Boltzmann Methods (LBM) as discretization strategies [1]. The resulting algorithms were implemented in a highly generic way in the non-commercial open-source framework OpenLB [2]. In the talk, particular focus is placed on the systematic approach of facing contemporary challenges in Computational Fluid Dynamics (CFD) [3, 4]. Further, the consideration of LBM as a generic technique for the approximation of Partial Differential Equations (PDE) [5] and its implementation on heterogeneous HPC-platforms are highlighted. The presented approaches and realizations are illustrated by means of various fluid flow simulation and optimization examples, where specific aspects are discussed for the simulation of particulate [6] and turbulent flows [7].


[1] Krause, M.J., 2010. Fluid Flow Simulation and Optimisation with Lattice Boltzmann Methods on High Performance Computers - Application to the Human Respiratory System, url:

[2] Krause, M.J., Kummerländer, A., Avis, S.J., Kusumaatmaja, H., Dapelo, D., Klemens, F., Gaedtke, M., Hafen, N., Mink, A., Trunk, R. and Marquardt, J.E., 2020. Openlb—Open source lattice Boltzmann code. Computers & Mathematics with Applications, doi: 10.1016/j.camwa.2020.04.033.

[3] Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E. and Mavriplis, D., 2014. CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences, NASA Technical Report, no. NASA/CR-2014-218178, url:

[4] Kwak, D., Kiris, C. and Kim, C.S., 2005. Computational challenges of viscous incompressible flows. Computers & Fluids, 34(3), pp.283-299, doi: 10.1016/j.compfluid.2004.05.008.

[5] Simonis, S., Frank, M. and Krause, M.J., 2020. On relaxation systems and their relation to discrete velocity Boltzmann models for scalar advection–diffusion equations. Philosophical Transactions of the Royal Society A, 378(2175), p.20190400, doi: 10.1098/rsta.2019.0400.

[6] Trunk, R., Weckerle, T., Hafen, N., Thäter, G., Nirschl, H., Krause, M.J., 2021. Revisiting the homogenized lattice Boltzmann method with applications on particulate flows, Computation 9 (2), p. 11, doi: 10.3390/computation9020011

[7] Haussmann, M., Ries, F., Jeppener-Haltenhoff, J.B., Li, Y., Schmidt, M., Welch, C., Illmann, L., Böhm, B., Nirschl, H., Krause, M.J. and Sadiki, A., 2020. Evaluation of a Near-Wall-Modeled Large Eddy Lattice Boltzmann Method for the Analysis of Complex Flows Relevant to IC Engines. Computation, 8(2), p.43, doi: 10.3390/computation8020043.

10:30am - 10:50am

Multi-architecture implementation of Adaptive Mesh Refinement for Lattice-Boltzmann Method


1Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique de Fluides, Gif-sur-Yvette F-91191, France; 2Université Paris-Saclay, CEA, Maison de la Simulation, Gif-sur-Yvette F-91191, France

The research work presented herein proposes an implementation of a Lattice Boltzmann Method [1] (LBM), coupled with an Adaptive Mesh Refinement (AMR) algorithm, with main focus on the portability and the optimisation of the code on different high performance computing (HPC) architectures. To preserve the efficiency of LBM for HPC when using the adaptive grid, as well as to optimally exploit the available HPC resources and keep up-to-date with their progress, the developed computational tool is built atop of Kokkos [2] C++ library for scientific computing. Kokkos handles automatically the adaptation and optimisation of a single piece of software on different computer architectures, such as CPUs, GPUs, shared and distributed memory systems alike.

The proposed method uses the BGK collision operator but alters the streaming step. Instead of using multiple time-steps [3], a single time-step with a Lax-Wendroff [4] spatial discretisation scheme is employed, which accommodates computational cells of different sizes, while sub-iterations per computation step or variable scaling are avoided, and data sweeps and exchanges are minimised. The computational domain is discretised by a cell-centred mesh, which is organised in a block-based octree structure. Computations, as well as refinement and coarsening operations, are performed on each block separately. Block communication and boundary condition imposition are realised through layers of ghost cells filled by quadratic polynomial interpolations. Preliminary assessment and validation tests, on transport problems of a Gaussian distribution profile, for which analytical solutions exist, show that the AMR approach with respect to a fully refined uniform mesh simulation, can reduce the total number of computational cells, and therefore the mean time of a single computational iteration, 5 times, without loss of accuracy. In addition, hard disk I/O processes get accelerated. The normalised gradient of the concentration was used as a refinement criterion and coarsening occurred automatically on neighbouring blocks that did not require refinement.

These encouraging results, indicate the great potential of the method's application on more complex physical problems, such as porous media or multiphase flows and dissolution modelling, coupled with Navier-Stokes equations.


[1] Timm Krüger, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, and Erlend Magnus Viggen.The lattice boltzmann method.Springer International Publishing, 10(978-3):4–15, 2017.

[2] H. Carter Edwards, Christian R. Trott, and Daniel Sunderland. Kokkos: Enabling manycore performance porta-bility through polymorphic memory access patterns.Journal of Parallel and Distributed Computing, 74(12):3202– 3216, 2014. Domain-Specific Languages and High-Level Frameworks for High-Performance Computing.

[3] D. Lagrava, O. Malaspinas, J. Latt, and B. Chopard. Advances in multi-domain lattice Boltzmann grid refinement.Journal of Computational Physics, 231(14):4808–4822, 2012.

[4] Abbas Fakhari, Martin Geier, and Taehun Lee. A mass-conserving lattice Boltzmann method with dynamic gridrefinement for immiscible two-phase flows.Journal of Computational Physics, 315:434–457, 2016

10:50am - 11:10am

Neural Lattice Boltzmann Method for Machine-Learning Enhanced Simulations

Bedrunka, Mario Christopher1,2; Wilde, Dominik1,2; Krämer, Andreas3; Reith, Dirk1,4; Foysi, Holger1

1University of Siegen; 2Bonn-Rhein-Sieg University of Applied Sciences; 3Freie Universit¨at Berlin; 4Fraunhofer Institute for Algorithms and Scientific Computing

The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. It is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques. For this reason we present a possible connection between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch’s deep learning facility. As a proof

of concept for combining machine learning with the LBM, a neural collision model is developed and trained on different flows.

11:10am - 11:30amCoffee Break
11:30am - 12:30pmTurbulent flow
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Li-Shi Luo, CSRC
11:30am - 11:50am

A lattice-Boltzmann solver coupled to an immersed boundary method with applications to turbulent flows

Cheylan, Isabelle; Favier, Julien; Sagaut, Pierre

Aix Marseille Univ, France

An immersed boundary method is coupled to a turbulent wall model and Large Eddy Simulation, with a Lattice-Boltzmann solver based on the Hybrid Recursive Regularized (HRR) collision model. The method is able to handle arbitrarily moving objects immersed at high Reynolds number flows and to accurately capture the shear layer and near wall effects.

When dealing with high Reynolds number turbulent wall-bounded flows, modeling near wall turbulence, and more precisely the inner layer of the turbulent boundary layer, becomes a primary concern in many industrial fields, since this part of the flow governs most of the friction and heat/mass transfers at the wall. In this work, the power wall law, which is an explicit wall model without any iterative procedure for the determination of the friction velocity, is combined with the immersed boundary method (IBM).

The IBM consists of defining a volume force term on the boundary between the fluid and the solid, calculated to satisfy the no-slip boundary condition at the wall. For the LBM, the recently developed Hybrid Recursive Regularized (HRR) model is used to enhance numerical stability and the algorithms are implemented within the ProLB software.

We perform a thorough numerical study to validate and characterize the efficiency, stability and accuracy of the numerical framework using a set of test-cases of increasing complexity. The robustness and accuracy of the method are assessed first in a static laminar configuration, then in a mobile laminar case, and finally in a static and oscillating turbulent simulation. In all cases, the proposed method shows good results compared to the available data in the literature.

11:50am - 12:10pm

Large-Eddy Simulation of an axisymmetric and isothermal jet developing in a room based on the Lattice Boltzmann Method

GRESSE, Teddy1; MERLIER, Lucie2; JACOB, Jérôme3; KUZNIK, Frédéric1

1Univ Lyon, INSA Lyon, CNRS, CETHIL UMR5008, Villeurbanne, F-69621, France; 2Univ Lyon, UCBL, INSA Lyon, CNRS, CETHIL UMR5008, Villeurbanne, F-69621, France; 3Aix Marseille Univ, CNRS, Centrale Marseille, M2P2 UMR 7340, Marseille, 13451, France

Convective flows induced by HVAC (Heating, Ventilation and Air Conditioning) systems play an important role in the thermal comfort of buildings. However, they are particularly difficult to predict because they are not fully turbulent and interact with their environment.

In order to better predict and understand these complex flows, this contribution presents the validation of Large Eddy Simulations (LES) [1] of an axisymmetric and isothermal jet developing in a room near a wall. Although rarely used in building applications, mainly due to its high computational cost, LES provides more detailed and accurate predictions of interior flows compared to statistical models (RANS - Reynolds Averaged Navier-Stokes) [2]. Moreover, this study is based on the Lattice-Boltzmann Method (LBM) [3] and the ProLB software [4]. This framework allows for massively parallel computations and easy preprocessing of complex geometries. Therefore, the approach chosen allows to efficiently perform detailed and high-fidelity simulations of complex environments.

The simulations are validated and calibrated using an extensive experimental data set of a full-scale mechanically ventilated test room called MINIBAT [5]. To this end, numerical results are compared with experimental data in terms of vertical and lateral jet expansion rates, mean velocity profiles within the jet and turbulent quantities. The results show a good qualitative and quantitative agreement between numerical and experimental data: the anisotropy of the jet expansion is well recovered and the shapes of the profiles as well as the maximum values of the mean velocity are consistent with experiment. Also, a qualitative analysis of the jet turbulence distribution is performed through the observation of Lumley triangles and the visualization of turbulent structures with vorticity contour plots. The analysis reveals that the main turbulent mechanisms in the jet development zone are well captured. Hence, the modelling approach adopted is suitable for the intended building application.

This work should be extended to anisothermal jet simulations to study thermal effects coupled with turbulence. It is also intended to couple the simulation of the hot jet with a high resolution building energy simulation [6]. The coupling will enable more realistic dynamic boundary conditions at the room walls to evaluate the dynamics of heat transfers and thermal comfort.

[1] P. Sagaut, Large Eddy Simulation for Incompressible Flows: An Introduction, Springer, 2006.

[2] B. Blocken, “LES over RANS in building simulation for outdoor and indoor applications: A foregone conclusion?,” Building Simulation, 2018.

[3] T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva and E. M. Viggen, The Lattice Boltzmann Method - Principles and Practice, Springer, 2016.

[4] “,” [Online].

[5] F. Kuznik, “Etude expérimentale des jets axisymétriques anisothermes horizontaux se développant près d’une paroi: application à la modélisation numérique des cavités ventilées,” PhD Thesis, INSA, Lyon, 2005.

[6] T. Gresse, L. Merlier, J.-J. Roux and F. Kuznik, “Development of a 3D and high resolution dynamic thermal model of a room with sun patch evolution for thermal comfort applications,” Building Simulation Conference Proceedings, 2021.

12:10pm - 12:30pm

Why is it still difficult to simulate turbulent two-phase flow at high density ratios with the lattice Boltzmann method?

Geier, Martin; Kutscher, Konstantin

TU Braunschweig, Germany

The lattice Boltzmann method is often claimed to be particularly well suited for the simulation of two-phase flows but simulating flows at the technically most relevant density ratio of the water/air system has remained difficult even after many promising proposals. Even though significant density ratios can be obtained in some models, their range of admissible Reynolds numbers is usually drastically reduced when compared to single phase models. Recent proposals to eliminate the strong gradients in momentum by switching to a velocity-based formulation lead to mixed results. In the velocity-based formulation the pressure is replaced with the normalized pressure (i.e. the pressure divided by density) which introduces a new discontinuity into the equation. Proposed solutions include the complete elimination of the pressure from the lattice Boltzmann equation which then needs to be supplemented by an external pressure solver. Another solution is to limit the simulations to very small pressure differences to keep the gradients in normalized pressure small enough to compensate for them by simple finite difference corrections. However, these corrections deteriorate quickly if the pressure is not extremely small. The reason for this is that the pressure term in the velocity-based Navier-Stokes equation is not conservative and that the implementation of non-conservative operators is generally difficult in the LBM. In this contribution we explore a new way of implementing non-conservative operators in the lattice Boltzmann framework and apply it to the pressure term in the velocity-based phase field LBM.

12:30pm - 2:00pmLunch
Location: Room MSI 218, Maison des Sciences de l'Ingénieur (MSI), La Rochelle University
2:00pm - 3:20pmMultiphase and Porous Media Flows etc.
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Catherine Choquet, La Rochelle University
2:00pm - 2:20pm

A lattice Boltzmann study of miscible displacement process with precipitation reaction in porous media

Liu, Gaojie1,2; Shao, Ziyu1,2

1School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China, People's Republic of; 2Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai 200093, China, People's Republic of

The miscible displacement process with precipitation reaction in porous media widely exists in many fields such as the formation of submarine hydrate, underground storage of CO2, solidification of metal materials, Liesegang phenomenon and so on. In this process, the coupling of flow, diffusion, reaction and the continuous change of solid structure caused by precipitation, makes the overall process very complex. In this work, the miscible displacement process with precipitation reaction is simulated. The time evolutions of fluid concentration field are observed, and the effect of precipitation reaction on displacement process is compared with the one without precipitation reaction. Then, the changes of porosity and displacement efficiency are studied by changing the relevant dimensionless parameters, the following conclusions are obtained: the precipitation reaction will generate crystal hydrate on the surface of the solid framework of porous media, and the continuous expansion of the solid structure will hinder the displacement process; The greater the Da number, the more hydrate will be generated, and the smaller the displacement efficiency will be. However, when the Da number increases to a certain value, the displacement process cannot be carried out.


This study is supported by the National Natural Science Foundation of China (Grant No. 51806142), Shanghai Sailing Program (Grant No. 18YF1418000).

2:20pm - 2:40pm

A lattice Boltzmann study on displacement processes of thermal miscible fluids with density gradient in porous media

Wang, Yongqiang; Liu, Gaojie

School of Energy and Power, University of Shanghai for Science and Technology, China, People's Republic of

Thermal miscible fluid displacements in porous media widely exist in industry process, such as carbon dioxide storage, fuel cell and chemical industry. In thermal miscible displacement process, the displacement front sharp changes because of temperature difference, viscosity difference and, density gradient. It should be noted that the gravity gradient is also one of the important factors affecting displacement efficiency. However, most of researchers have overlooked it.

In this work, a numerical study of the displacement process of thermal miscible fluids with density gradient in a porous medium is carried out. A lattice Boltzmann method (LBM) is used to simulate the displacement process because of its advantages in simulating flow in porous media. The effects of different Rayleigh number (Ra), inclination angle (θ) and viscosity ratio (M) on interface shape, displacement efficiency and the scalar dissipation of the fluids are quantitatively analyzed. The results show that: under the positive inclination angle, the larger the inclination angle, the stronger the fluid instability and the greater the displacement efficiency, the less sufficient the mixing of two fluids; the fluid flow state and the displacement efficiency are not sensitive to the negative inclination angle. With the increase of the viscosity ratio, the formation of the instability phenomenon of "Kelvin–Helmholtz" and "rolling up" will be accelerated, thereby improving the displacement efficiency. The increase of the Rayleigh number increases the fluid instability and the displacement efficiency.


This study is supported by the National Natural Science Foundation of China (Grant No. 51806142), Shanghai Sailing Program (Grant No. 18YF1418000).

2:40pm - 3:00pm

Geochemical digital twin: Mesoscopic modeling of counter-diffusion experiments for resolving carbonate precipitation mechanisms in porous media

Peng, Haonan1,3; Mokos, Athanasios1; Rajyaguru, Ashish1,2; Curti, Enzo1; Grolimund, Daniel2; Churakov, Sergey1,3; Prasianakis, Nikolaos1

1Laboratory for Waste Management, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland; 2Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland; 3Institute of Geological Sciences, University of Bern, CH-3012 Bern, Switzerland

Mechanistic understanding of calcium carbonate precipitation polymorphs (calcite, vaterite, aragonite) is a challenging research problem due to the complexity of the process which is dictated by the interplay of nucleation, crystallization, precipitation kinetics, species transport, homogeneous and heterogeneous chemical reactions. During experimental investigations and in order to decipher the governing mechanisms, it is necessary to obtain in detail the time evolution of the major diffusion pathways and the local conditions at the solid-fluid interfaces during the crystal growth. For this purpose, the digital twin of a laboratory experiment is developed. The D3Q27 multi-component lattice Boltzmann method (LBM) is used as the basis framework for simulating the reactive transport processes in porous media at the pore scale. It enables to obtain information at very high spatial and temporal resolution and to incorporate all necessary physical and chemical processes [1]. The experimental observations at the synchrotron facilities of the Swiss Light Source (SLS PSI), in combination with numerical modeling results will allow us to correlate the type of polymorph precipitated with the saturation state and local composition of the aqueous solution. The preliminary model is tested by simulating the precipitation process of calcium carbonate with different Damköhler numbers which resulted in different morphology of precipitates. For efficient simulations, two levels of acceleration are needed. First, the computationally expensive geochemical solver can be replaced during the simulations by a neural network based metamodel [2]. Second, the code is accelerated even further by using a hybrid CUDA-MPI programming layout which can be executed on several GPUs in parallel, in this case at the Swiss Super Computing Center (CSCS).

[1] Prasianakis, N.I., Curti, E., Kosakowski, G., Poonoosamy, J, Churakov, S.V., Deciphering pore-level precipitation mechanisms, Scientific Reports, 7(1), 13765 (2017)

[2] Prasianakis, N. I., Haller, R., Mahrous, M., Poonoosamy, J., Pfingsten, W., & Churakov, S. V. (2020) Neural network based process coupling and parameter upscaling in reactive transport simulations. Geochimica et Cosmochimica Acta 291, 126-143

3:00pm - 3:20pm

Lattice Boltzmann Model of fluid flow in porous media: tortuosity and porosity effects

D’Orazio, Annunziata; Karaimipour, Arash; Ranjbarzadeh, Ramin

Sapienza University of Rome, Italy

In this work fluid flow through porous media has been modeled by means of the second-order lattice Boltzmann method (LBM). Pore-Scale (PS) method has been used to simulate a porous channel with different porosity degrees by placing square obstacles into the channel. Different arrangements of the obstacles (in-line, staggered and random configurations) differently sized determine porosity and tortuosity factors of porous media.

The velocity-based method has been used to calculate the tortuosity for four configurations of obstacles, different Reynolds numbers from 30 to 300 and a wide range of porosities 0.65, 0.75, 0.85 and 0.95.

Tortuosity values were computed after modeling the velocity field under the effect of mentioned effective parameters. Finally, we found that a possible forward step in this field of study can be varying the configuration of obstacles with the same porosity factor. Pressure drops are evaluated as a function of porosity and tortuosity factor. In addition, with the same obstacle shape and porosity factor, if we change the angle of the obstacles, we can achieve higher tortuosity values.

3:20pm - 3:40pmCoffee Break
3:40pm - 5:20pmPoster Session
Location: Room MSI 218, Maison des Sciences de l'Ingénieur (MSI), La Rochelle University
Session Chair: Christophe Saint-Jean, La Rochelle University
3:40pm - 4:00pm

Thermodynamics of multiple cavitation bubbles interaction with lattice Boltzmann method

He, Xiaolong1; Zhang, Jianmin2; Peng, Haonan3; Yuan, Hao1

1Chongqing Jiaotong University, China, People's Republic of; 2Sichuan University, China, People's Republic of; 3Laboratory for Waste Management, Paul Scherrer Institute, CH, 5232, Villigen PSI, Switzerland

An improved double distribution function (DDF) thermal lattice Boltzmann method is applied to investigate the thermodynamics of multiple bubbles interaction. This model is validated by simulating the evolution process of a laser-produced bubble, and both qualitative and quantitative verification is carried out by comparing with the experimental result and theoretical analysis. The interactions between two vapor bubbles during the collapse process are simulated, and the hydrodynamics and thermodynamics of the cavitation bubble under different influence factors (ie., bubble radius, the distance between two bubbles) are systematically investigated. An attempt was made to give a critical distance to distinguish the weak interaction and strong interaction. Furthermore, the thermodynamics of the bubble cluster is also investigated. The hydrodynamics and thermodynamics during the collapse process in different regions of the cavitation bubble cluster are given. The shielding effect in the outer bubble and the wall effect in the inner bubble is accurately reproduced. Moreover, the temperature superposition effect during the clustered cavitation bubbles collapse process is also proposed.

4:00pm - 4:20pm

Computer simulations of the lymphatic vessels and valves dynamics

Bou Orm, Alaa; Kaoui, Badr

Biomechanics and Bioengineering Laboratory, CNRS, Universite de Technologie de Compiegne, Compiegne, France

The lymphatic system consists of initial lymphatic vessels, which absorb lymph liquid, and collecting lymphatic vessels, which transport the lymph through the lymphatic network and its nodes. The lymph pumping mechanisms is achieved by a cyclic of compression and expansion of the lymphatic vessel wall forced by the surrounding muscles. The lymphatic valves allow pumping the lymph and they prevent its backflow.

We are developing fully coupled two-dimensional fluid-structure computational model to study effects of various parameters on the mechanical behavior of the valves. The lattice Boltzmann method is used to compute the lymph fluid flow and the immersed boundary method to couple the lymph flow with the mechanics of multiple lymphangions and their bicuspid lymphatic secondary valves.

4:20pm - 4:40pm

Assessment of collision operators and forcing schemes in the pseudo-potential lattice-Boltzmann method

Restrepo Cano, Juan Guillermo1; Hernandez Perez, Francisco E.1; Lei, Timan2; Luo, Kai2; Im, Hong G1

1King Abdullah University of Science and Technology, Saudi Arabia; 2University College London, United Kingdom

In this work, a multiphase pseudo-potential lattice-Boltzmann (PP-LB) model was implemented to compare the numerical performance of different collision operators and forcing schemes in terms of the spurious velocities, accuracy, and computational cost. The single-relaxation time (SRT), the 2nd and 3rd-order multi-relaxation time (MRT), and the central moment (CM) collision operators are included in the comparison. In addition, the exact difference method (EDM) was incorporated, along with two improved formulations for Guo’s forcing scheme, as proposed by Li et al. (2012) and Huang & Wu (2016), that satisfy the mechanical stability condition. The different combinations of collision operators and forcing schemes were studied using the Carnahan-Starling (CS) and Peng-Robinson (PR) equations of state (EOS) for a two-dimensional stationary droplet. The predicted equilibrium densities given by the PP-LB method show a remarkable agreement with the theoretical coexistence curve and the coexistence curves predicted by Li et al. (2012). The relative error of the predicted values using the PP-LB model with respect to the theoretical coexistence curve did not exceed 2% for both EOS when the EDM and improved Guo’s schemes were employed. Furthermore, by comparing the numerical performance of the so-called β-scheme for computing the Shan & Chen’s interaction force with the standard Guo’s scheme, it is found that, despite a positive impact on accuracy and reducing spurious currents, it is unstable at reduced temperatures (Tr) below 0.76, whereas the improved forcing schemes that satisfy the mechanical stability condition are stable at Tr ≥ 0.66.

4:40pm - 5:00pm

Accuracy of SYCL implementations of Lattice Boltzmann Methods for Fluid Flow

Muite, Benson1; Mahdi Tekitek, Mohamed2

1Kichakato Kizito; 2Université de Tunis El Manar

The SYCL standard promises portability of programs on a variety of hardware including central processing units, graphical processing units and field programmable gate arrays. The speed of different operations on depends on the hardware platform chosen. The main aim of this contribution is to examine accuracy as a function of time to solution for lattice boltzmann schemes that approximate laminar incompressible two dimensional fluid flow on a single device.

5:00pm - 5:20pm

Modeling Shrinking Biomass Pyrolysis using the REV-Scale 3-D Lattice Boltzmann Method

Cho, Yongsuk1; Kong, Song-Charng2

1Iowa State University, United States of America; 2Texas Tech University, United States of America

Biomass pyrolysis is a useful thermal decomposition method of converting low-energy value materials to fuel by breaking down a complex organic structure in an oxygen-deficient environment. It is known that the macroscopic transport equations have intrinsic limitations to accurately modeling the pyrolysis because sub-particle level phenomena alter the pyrolysis regime. For bridging the micro-scale and macro-scale phenomena, the Representative Elementary Volume (REV)-scale Lattice Boltzmann (LB) method is presented to resolve the fluid, heat, and mass transfer in both the biomass particle and the gas phase. The recently developed conjugated heat transfer LB model is adapted to model the heat transfer at the solid-gas interface. Additionally, a particle contraction method is formulated to simulate the effect of biomass shrinkage. Experiments are used to validate the three-dimensional numerical results. The predicted temperature profile and the mass loss of biomass agree well with the experimental data. The REV scale simulation shows that a linear Darcy regime governs the inside biomass flow, and the pressure build-up is detected. It was found that the variable Internal thermal conductivity is the most important parameter to accurately model the pyrolysis. The results illustrate that the biomass shrinkage accelerates particle conversion and increases the tar yield. A parametric study indicates that the increased biomass size adversely affects the overall tar yield due to the acceleration of the secondary reaction.

Date: Wednesday, 29/June/2022
8:30am - 9:30amInvited speaker
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University

The Saga of the LBE's Quest for Rarefied Gas Effects

Luo, Li-Shi

CSRC, China, People's Republic of

The Saga of the LBE's Quest for Rarefied Gas Effects

9:30am - 10:50amHigh Performance Computing LBM Implementation
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Martin Geier, TU Braunschweig
9:30am - 9:50am

GPU implementation of a discrete unified gas kinetic scheme for low-speed isothermal flows

Liu, Peiyao1; Huang, Changsheng2; Guo, Zhaoli1

1State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, China; 2School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan, China

A general purpose discrete unified gas kinetic scheme (Guo et al., 2013 Phys. Rev. E) implementation for low-speed isothermal flows is developed on a single Graphics Processing Unit (GPU). The implementation has been validated by simulating lid-driven cavity flow. The parallel performance improves significantly using the newly implemented approach. Compared with CPU serial calculation method, a speedup of 30 times of magnitudes has been found. The results show that the parallel GPU provides an affordable alternative to large clusters for fluid dynamics prediction.

9:50am - 10:10am

GPU on non-uniform meshes: a modern implementation approach and detailed decomposition of performance

Latt, Jonas; Coreixas, Christophe

University of Geneva, Switzerland

We revisit the topic of mesh refinement on GPU in the lattice Boltzmann (LB) method by adopting a straightforward implementation approach based on C++17 Parallel Algorithms. The general usefulness of this approach for GPGPU implementation of LB codes had previously been explored using the open-source demo code STLBM [1] ( More recently, modifications were made to the open-source library Palabos [2] so that simulations based on single and multiple GPUs could be possible thanks to its already existing MPI backend ( While the latter works were restricted to uniform meshes, this talk further discusses how to extend the above methodology to non-uniform grids based on quad-tree refinement algorithms. To establish a baseline for the analysis of the performance to be expected from a non-uniform GPU LB code, the straightforward grid-refinement approach by Rohde et al [3] is used which, at large Reynolds numbers, can lead to results of comparatively good quality. This is illustrated in the case of a flow around a high-lift airfoil and in the case of an air flow over a cavity, with acoustic effects.

Very interestingly, we show that through application of a memory saving neighbor-link implementation to incompressible flow simulations, a non-uniform mesh performs only slightly less well than a uniform one in terms of raw cell-processing performance, with a performance loss (in lattice-site updates per second) of 25% at single precision and 10% at double precision. In a second stage, we explore the extension of the approach to multi-speed, compressible flow simulations.

[1] Latt et al. Cross-platform programming model for many-

core lattice Boltzmann simulations. Plos One (2021).

[2] Latt et al. Palabos: Parallel Lattice Boltzmann Solver. CAMWA (2021).

[3] Rohde et al. A generic, mass-conservative local grid refinement technique for lattice Boltzmann schemes. Int. J. Num. Meth. Fluids (2006).

10:10am - 10:30am

HPC Performance study of different collision models using the Lattice Boltzmann solver Musubi

Spinelli, Gregorio Gerardo1; Masilamani, Kannan1; Horstmann, Tobias2; Soni, Malav3; Klimach, Harald Günther1; Stück, Arthur1; Roller, Sabine1

1DLR, German Aerospace Center, Institute of Software Methods for Product Virtualization, Dep. of Simulation Frameworks, Zwickauer Straße 46, 01069 Dresden, Germany; 2DLR, German Aerospace Center, Institute of Propulsion Technology, Dep. of Engine Acoustics, Bismarckstraße 101, 10625 Berlin, Germany; 3DLR, German Aerospace Center, Institute for Aerodynamics and Flow Technology, Dep. of Technical Acoustics, Lilienthalplatz 7, 38108 Braunschweig, Germany

Lattice Boltzmann (LB) solvers have gained much attention in the last decades as an alternative approach to the classical Navier-Stokes solvers. The open-source LB solver “Musubi” is designed for scale resolving CFD. Key features are good scalability on HPC systems, static mesh refinement and advanced collision models such as Cumulant and Hybrid Recursive Regularized BGK. We will showcase the application of Musubi to solve aerodynamics and aeroacoustics fields using two test cases: the flow around the cylinder at Reynolds number (Re) = 3900 and the Boeing rudimentary landing gear (RLG) defined on the 2010 BANC-I workshop at a wheel Re = 10^6, for which we could achieve a stable simulation at Re = 10^5. While the cylinder case is used to validate different collision models, the RLG case will provide insights into performance and scalability characteristics of the different collision models in conjunction with a typical target configuration on state-of-the-art HPC systems. Additionally, we will use the RLG case to present its competitiveness in terms of performance and scalability.

10:30am - 10:50am

High-accuracy curved lattice Boltzmann boundary conditions for efficient GPU simulations

Marson, Francesco1; Ginzburg, Irina2; De Santana Neto, José Pedro1; Silva, Gonçalo3; Latt, Jonas1

1University of Geneva, Switzerland; 2University Paris-Saclay, INRAE, France; 3University of Évora, Portugal

With the lattice Boltzmann Method (LBM), a straightforward extension of the bounce-back no-slip rule leads to a vast group of directional (aka link-wise) Dirichlet boundary conditions. These methods can accurately describe the interaction of a fluid flow with a complex solid surface in a uniform Cartesian grid.

The link-wise family includes an infinite number of schemes that can be tuned to optimize their five fundamental features: (i) exactness of channel flows velocity and pressure profiles, (ii) accuracy order, (iii) linear stability, (iv) parametrization, and (v) locality.

We identify, respectively, two main groups of directional schemes. The first comprises compact schemes with linear exactness (LI) (Ginzburg et al., 2008) and its extended local (ELI) family (Ginzburg et al., 2022; Marson, 2022; Marson et al., 2021), which combines the local single-node implementation with the second-order accuracy, linear exactness, and physical consistency. The second is the Multi-reflection (MR) family, which gains parabolic exactness in the Stokes and Navier-Stokes flows but loses locality.

This presentation focuses on the new developments of ELI, which provide ELI (and LI) with parabolic exactness in Stokes flows. Additionally, it shows how these schemes allow for simple and uniform implementations, even in the coarsest simulations characterized by many narrow gaps.

One can implement ELI simply by modifying the collision model in the boundary node where the half-way bounce-back (HW) applies. Therefore, the implementation in a high-performance code is straightforward. We implement ELI in GPU-accelerated Palabos (Latt et al., 2021a, 2021b), which allows for multi-GPU simulations, showing that one can obtain outstanding numerical performances which are close to the ones of the HW for steady boundaries.

Ginzburg, I., Silva, G., Marson, F., Chopard, B., Latt, J., 2022. Unified directional parabolic-accurate Lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows. Phys. Rev. E Submitted. 51.

Ginzburg, I., Verhaeghe, F., d’Humières, D., 2008. Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure and Mixed Boundary Conditions. Commun Comput Phys 3, 427–478.

Latt, J., Malaspinas, O., Kontaxakis, D., Parmigiani, A., Lagrava, D., Brogi, F., Belgacem, M.B., Thorimbert, Y., Leclaire, S., Li, S., Marson, F., Lemus, J., Kotsalos, C., Conradin, R., Coreixas, C., Petkantchin, R., Raynaud, F., Beny, J., Chopard, B., 2021a. Palabos: Parallel Lattice Boltzmann Solver. Comput. Math. Appl., Development and Application of Open-source Software for Problems with Numerical PDEs 81, 334–350.

Latt, J., Marson, F., De Santana Neto, J.P., Thyagarajan, K., Coreixas, C., Chopard, B., 2021b. From CPU to GPU in 80 days.

Marson, F., 2022. Directional lattice Boltzmann boundary conditions.

Marson, F., Thorimbert, Y., Chopard, B., Ginzburg, I., Latt, J., 2021. Enhanced single-node lattice Boltzmann boundary condition for fluid flows. Phys. Rev. E 103, 053308.

10:50am - 11:10amCoffee Break
11:10am - 12:30pmAlgorithm and Applications
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: François Dubois, CNAM & Univ. Paris-Saclay
11:10am - 11:30am

Non-uniform force effect in lattice Boltzmann methods for Poiseuille flows

Chang, Hung-Wen; Garg, Anshul; Lin, Chao-An

National Tsing Hua University, Taiwan

Various external forcing formulations of the lattice Boltzmann method (LBM) are analyzed by deriving the analytic solutions of the fully developed Poiseuille flows with and without the porous wall.

For uniform driving force, all the forcing formulations recover the second-order accurate discretized Navier-Stokes equation. However, the analytic solutions show that extra force gradients arise due to variable force, and this form differs from the analysis using Chapman-Enskog expansion.

It is possible to remove these extra terms of single-relaxation-time (SRT) LBM using specific relaxation time depending on the force formulation adopted. However, this limits the broader applicability of the SRT LBM. Moreover, the multiple-relaxation-time (MRT) LBM may provide an option to remove the variable-force gradient term benefiting from separating relaxation parameters for each moment.

11:30am - 11:50am

Compressible Semi-Lagrangian lattice Boltzmann method for three-dimensional viscous flows with body-fitted meshes

Wilde, Dominik1,2,3; Bedrunka, Mario1,2; Krämer, Andreas4; Reith, Dirk2; Foysi, Holger1

1University of Siegen, Germany; 2Bonn-Rhein-Sieg University of Applied Sciences, Sankt Augustin, Germany; 3University of California San Diego, La Jolla, CA, United States; 4Freie Universität Berlin, Germany

Off-lattice Boltzmann methods generally offer more flexibility than the customary lattice Boltzmann method, but at the price of higher computational costs. Nevertheless, features such as changeable time step sizes, body-matched meshes, or special velocity sets can be reasons for using off-lattice Boltzmann methods. As an alternative to finite difference or finite volume lattice Boltzmann methods, the semi-Lagrangian lattice Boltzmann method (SLLBM) has established itself as a competitive off-lattice Boltzmann method.

Semi-Lagrangian lattice Boltzmann methods follow the characteristics of the particle distribution functions back in time, similar to the original lattice Boltzmann method. However, when using time steps of a size other than one, when using non-standard velocity sets, or when using a non-Cartesian mesh, the advection step will not be from node to node. In this case, an interpolation step is required, and its implementation is crucial for the accuracy of the simulation. In our SLLBM approach, the simulation domain is discretized into cells, similar to the finite element method. Then, high-order shape functions are used to determine the particle distribution functions during the advection step. This procedure reduces mass losses of the interpolation and increases the overall accuracy.

In recent years, we have extended the SLLBM to simulate three-dimensional compressible viscous flows. Our ansatz was as follows: density, momentum, and temperature of the flow are simulated with one distribution function requiring a high-order expansion of the equilibrium up to fourth order. This also requires large velocity sets with high degree of quadrature, which usually makes the simulation too expensive. However, by using cubature rules for the velocity discretization, we have successfully reduced the size of velocity sets to only 45 discrete velocities in three dimensions. This paved the way for affordable 3D compressible simulations with the SLLBM.

In this contribution, we recapitulate the method, discuss advantages and disadvantages, and show recent results, e.g., viscous transonic and supersonic flows around 2D NACA airfoils and 3D spheres, both using body-fitted meshes.

11:50am - 12:10pm

Investigation of Liquid-Liquid Flow Patterns in a Y-Y channel using the Lattice Boltzmann Method

Sudha, Anand; Rohde, Martin

TU Delft, Netherlands, The

Microfluidic multiphase flow is a topic of increasing interest because of its applications and the possibilities it offers in various fields. The major advantages of operating in the microscale include the large surface-volume ratios, control of fluid flow and lower costs. Thus, it is imperative to study the flow patterns in such flows and the parameters which subsequently influence them. This research aims to examine the efficacy of LBM in simulating the flow of two immiscible fluids in a Y-Y channel by validating it with

experimental results and investigating the effect of dimensionless flow parameters and geometry on the flow patterns. The LBM can be easily extended to multiphase flow, and the interface need not be tracked in the case of multiphase LBM, thus retaining the simplicity of the single-phase model. This research uses the model proposed by Rothman and Keller to simulate multiphase flow (Gunstensen et al. [1991]). Particle

distributions are defined for each fluid in this method, and the interfacial tension is applied as a body force to ensure fluid separation. The case of two-phase flows in Y-Y channels is a little more complex than many earlier studies on multiphase LBM, primarily because of the range of velocities involved in the study. Previous studies dealing with multiphase channel flows have rarely taken the contact angle into account, and

when they have, it is for the simpler case of a rectangular or T-T channel. The problem is compounded by the inclination of the inlets and outlets, especially the corners located at the intersection of the inlets. This necessitates a different method of applying the contact angle. The method used in this research for implementing the contact angle was proposed by Xu et al (Xu et al. [2017]), where the contact angle is applied by correcting the position of the interface normal to match the contact angle. The complexity of this case, however, necessitates some modifications near the intersection of the inlets in the determination of the surface normal. Traditionally, an 8th order discretization is used to estimate the surface normal, but for certain boundaries, this introduces ambiguities as the boundary nodes might be located on either side of two fluid nodes. A lower-order discretization for these nodes is, therefore, necessary to avoid such ambiguities, which

is especially important when dealing with low Capillary numbers. At these values, traditionally slug flow is observed and at higher Capillary numbers, parallel flow is observed. The model is validated by comparing it to experimental results obtained by Liu (Liu [2022]) for various Capillary numbers. Simulations performed using the model were observed to accurately predict the flow regimes seen in the experiments. Additionally,

the length of the slugs obtained from the simulations was comparable to those from experiments. The phenomenon of leakage during parallel flow was also captured. Finally, the geometry of the channel is varied to understand the influence of geometry on the flow regimes and the capability of the method itself to model different geometries.


Bastien Chopard, Alexandre Dupuis, Alexandre Masselot, and Pascal Luthi. Cellular automata and lattice boltzmann techniques: An approach to model and simulate complex systems. Advances in complex systems, 5(02n03):103{246, 2002.

Andrew K. Gunstensen, Daniel H. Rothman, Stephane Zaleski, and Gianluigi Zanetti. Lattice Boltzmann model of immiscible fluids. Physical Review A, 43(8):4320{4327, 1991. ISSN 10502947. doi: 10.1103/PhysRevA.43.4320.

Zheng Liu. Purifying radionuclides with microfluidic technology for medical purpose. PhD Thesis, TU Delft Repository, 2022. doi:

Zhiyuan Xu, Haihu Liu, and Albert J Valocchi. Lattice boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media. Water Resources Research, 53(5):3770{3790, 2017.

12:10pm - 12:30pm

Lattice Boltzmann convection-diffusion model with non-constant advection velocity

Michelet, Jordan1,2; Tekitek, Mohamed Mahdi1; Berthier, Michel1

1MIA laboratory, La Rochelle University, 17000 La Rochelle; 2Bowen company, 91940 Les Ulis

The main objective of this contribution is to investigate Multiple Relaxation Time Lattice Boltzmann schemes for Convection-Diffusion Equations. In particular, we discuss the issue of obtaining second order exact schemes when the advection velocity is not constant.

Our study is based on previous results by the authors [1] that allow to identify the extra terms, coming from the non-constant advection velocity, that prevent the exactness of such shemes. We show how these terms can be cancelled, first by a suitable choice of the momentum equilibrium, and then by adding an ancillary distribution that acts as a forcing term applied to the non-conserved momentum. Numerical experiments are performed on Poiseuille and Taylor-Green test cases. They show that the proposed approaches are relevant regarding the stated problem.


[1] J. Michelet, M. M. Tekitek, and M. Berthier, “Multiple relaxation time lattice Boltzmann model for advection-diffusion equations with application to radar image processing,” Submitted in Journal of Computational Physics, dec 2021.

12:30pm - 2:00pmLunch
Location: Room MSI 218, Maison des Sciences de l'Ingénieur (MSI), La Rochelle University
2:00pm - 3:20pmMethod and Analysis I
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Paul Dellar, University of Oxford
2:00pm - 2:20pm

"A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme".

Caetano, Filipa2; Dubois, François1,2; Graille, Benjamin2

1LMSSC, CNAM Paris, France; 2LMO, Université Paris-Saclay, France

We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution towards the unique entropy solution by first estimating the supremum norm and the total variation of the discrete solution, and second by constructing a discrete kinetic entropy-entropy flux pair be-

ing given a continuous entropy-entropy flux pair of the hyperbolic system. We finally illustrate our results with numerical simulations of the advection equation and the Burgers equation.

2:20pm - 2:40pm

A comparative study of 3D Cumulant and Central Moments lattice Boltzmann schemes with interpolated boundary conditions for the simulation of thermal flows in high Prandtl number regime

Gruszczynski, Grzegorz1; Łaniewski-Wołłk, Łukasz2

1Warsaw University of Technology, Poland; 2School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, Australia

Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant–Friedrichs–Lewy condition, the numerical diffusion of the scheme has to be reduced. As a consequence, the numerical artefacts are dominated by the dispersion errors commonly known as wiggles. In this study, we explore possible remedies for these issues in the framework of lattice Boltzmann method by means of applying novel collision kernels, lattices with large number of discrete velocities, namely D3Q27, and a second-order boundary conditions.

For the first time, the cumulant-based collision operator, is utilised to simulate both the hydrodynamic and the thermal field. Alternatively, the advected field is computed using the central moments’ collision operator. Different relaxation strategies have been examined to account for additional degrees of freedom introduced by a higher order lattice.

To validate the proposed kernels for a pure advection-diffusion problem, the numerical simulations are compared against analytical solution of a Gaussian hill. The structure of the numerical dispersion is shown by simulating advection and diffusion of a square indicator function. Next, the influence of the interpolated boundary conditions on the quality of the results is measured in the case of the heat conduction between two concentric cylinders. Finally, a study of steady forced heat convection from a confined cylinder is performed and compared against a Finite Element Method solution.

It has been found, that the relaxation scheme of the advected field must be adjusted to profit from lattice with a larger number of discrete velocities, like D3Q27. Obtained results show clearly that it is not sufficient to assume that only the first-order central moments/cumulants contribute to solving the macroscopic advection-diffusion equation. In the case of central moments, the beneficial effect of the two relaxation time approach is presented [1].

- Reference:

[1] Gruszczyński, G., and Ł. Łaniewski-Wołłk. "A comparative study of 3D Cumulant and Central Moments lattice Boltzmann schemes with interpolated boundary conditions for the simulation of thermal flows in high Prandtl number regime." arXiv preprint arXiv:2203.01316 (2022).

2:40pm - 3:00pm

Finite Difference formulation of lattice Boltzmann schemes: consequences on consistency and stability

Bellotti, Thomas1; Graille, Benjamin2; Massot, Marc1

1CMAP, Ecole polytechnique, France; 2Institut de Mathématique d'Orsay, Université Paris-Saclay, France

Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. Despite the well-known advantages from a computational standpoint, this structure is not suitable to construct a rigorous notion of consistency with respect to the target equations and to provide a precise notion of stability. In order to alleviate these shortages and introduce a rigorous framework, we demonstrate that any “classical” lattice Boltzmann scheme can be rewritten as a corresponding multi-step Finite Difference scheme on the conserved variables. This is achieved by devising a suitable formalism based on operators, commutative algebra and polynomials. Therefore, the notion of consistency of the corresponding Finite Difference scheme, which can be studied without explicitly constructing this scheme, allows to invoke the Lax-Richtmyer theorem in the case of linear lattice Boltzmann schemes. Moreover, we show that the frequently-used von Neumann-like stability analysis for lattice Boltzmann schemes entirely corresponds to the von Neumann stability analysis of their Finite Difference counterpart. More generally, the usual tools for the analysis of Finite Difference schemes are now readily available to study lattice Boltzmann schemes. Our formalism could lead to a better understanding of other important topics, such as boundary conditions and initial conditions.

3:00pm - 3:20pm

Extended comparison between lattice Boltzmann and Navier-Stokes solvers for unsteady aerodynamic and aeroacoustic computations

Suss, Alexandre1; Mary, Ivan1; Le Garrec, Thomas1; Marié, Simon2,3

1DAAA, ONERA, Université Paris Saclay, F-92322 Châtillon - France; 2Laboratoire DynFluid, F-75013 Paris - France; 3Conservatoire National des Arts et Métiers, F-75003 Paris - France

Computational Fluid Dynamics (CFD) has become an important tool in aerospace sciences enabling both researchers and engineers to get more insight into complex fluid phenomena. The increasing computational power and the growing need of high-fidelity methods has lead to the development of Large Eddy Simulations (LES) tools among which structured finite-type Navier-Stokes (NS) methods and lattice Boltzmann methods (LBM) are the most promising ones to achieve industrial level computations [1]. Consequently, one question which naturally arises is: Which method is the most competitive, in terms of accuracy and computational cost, on canonical aerodynamic and aeroacoustic applications ?

Previous work on the comparison of the LBM with traditional NS methods focused on different topics such as convergence order [2], achievable error [3] and runtimes [4]. However, there still is a lack of fair one-to-one comparisons. Indeed, runtime-based results were obtained with two different solvers developed independently and having different levels of optimisation. In addition, the numerical properties of the lattice Boltzmann method are highly dependent on the collision operator [5] such that the conclusions of [3] have to be tempered.

This work aims at rigourously comparing a lattice Boltzmann solver with an LES-type finite-volume Navier-Stokes solver. The comparison takes place in ONERA's Cassiopée/Fast CFD environment implementing high-performance flow solvers relying on the same code architecture and optimisation layers. To do so, an extended von Neumann analysis of both lattice Boltzmann and Navier-Stokes schemes is proposed. The study is completed by numerical test cases to highlight the capabilities of each method. The implementation and computational times are also discussed. Finally, some trends about the performance of each methods are outlined.


[1] R. Löhner, “Towards overcoming the LES crisis,” Int. J. Comut. Fluid Dyn., vol. 33, no. 3, pp. 87–97, Mar. 2019.

[2] D. R. Noble, J. G. Georgiadis, and R. O. Buckius, “Comparison of accuracy and performance for lattice Boltzmann and finite difference simulations of steady viscous flow,” Int. J. Numer. Methods Fluids, vol. 23, no. 1, pp. 1–18, 1996.

[3] S. Marié, D. Ricot, and P. Sagaut, “Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics,” J. Comput. Phys., vol. 228, no. 4, pp. 1056–1070, Mar. 2009.

[4] K.-R. Wichmann, M. Kronbichler, R. Löhner, and W. A. Wall, “A runtime based comparison of highly tuned lattice Boltzmann and finite difference solvers,” Int. J. High Perform. Comput. Appl., pp. 370–390, Apr. 2021.

[5] G. Wissocq, C. Coreixas, and J.-F. Boussuge, “Linear stability and isotropy properties of athermal regularized lattice Boltzmann methods,” Phys. Rev. E, vol. 102, no. 5, p. 053305, Nov. 2020.

3:20pm - 3:40pmCoffee Break
3:40pm - 5:00pmThermal and Compressible Flows etc.
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Ezeddine Sediki, Faculty of Science of Tunis- University of Tunis El Manar
3:40pm - 4:00pm

Fluid-Structure Interaction coupled to transport phenomena: Biomedical applications

Kaoui, Badr

Biomechanics and Bioengineering Laboratory, CNRS, Universite de Technologie de Compiegne, Compiegne, France

We propose numerical schemes to tackle problems that involve fluid-structure interaction coupled to transport phenomena. We use the lattice Boltzmann method to compute fluid flow as well as advection-diffusion-reaction of chemical entities. We compute structure dynamics using the spring model and we couple it to transport phenomena using the immersed boundary method. We propose also an algorithm to implement unsteady jump boundary condition to deal with mass transfer across moving deformable boundaries that exhibit resistance and discontinuity in concentration. As applications, we show briefly results obtained for drug delivery from particles subjected to flow, performance of an artificial pancreas-on-chip, and biochemically induced oscillations of the lymphatic vessels walls.

4:00pm - 4:20pm


Peng, Yan; Armstrong, Charles

Old Dominion University, United States of America

In this work a numerical method for fully three dimensional simulations of capsules in the electrohydrodynamic regime is proposed. A quasi-steady dual time-stepping scheme allows for iterative computation of the capsule's fluid velocity using the multigrid lattice Boltzmann method at each time step. The capsule's elasticity is computed using a linear finite element method and the membrane's bending resistance is computed from the Helfrich bending energy. The immersed interface method (IIM) is used to compute the electric field arising due to the electrical properties of the interior fluid, exterior fluid, and the membrane. The fluid structure interaction is facilitated through the immersed boundary method (IBM), which is coupled to the IIM through least squares interpolation between the control points of the IIM and the Lagrangian nodes of the IBM. The method is validated by comparing the numerical results to analytical solutions and previously published studies. The method is then used to study the deformation of capsules in a combined shear flow and DC electric field for various membrane conductances, membrane capacitances, and conductivity ratios. For nonconducting membranes the interaction between the distribution of the electric forces and the capsule inclination angle due to the shear flow result in complex equilibrium dynamics not reported for neutral capsules.

4:20pm - 4:40pm

Simulations of boiling flow on the heterogeneous surface of a nuclear reactor fuel assembly system

Mokos, Athanasios1; Patel, Ravi Ajitbhai2; Peng, Haonan1,3; Karalis, Konstantinos3; Churakov, Sergey1,3; Prasianakis, Nikolaos1

1Laboratory for Waste Management, Paul Scherrer Institute, Switzerland; 2Institute of Concrete Structures and Building Materials, Karlsruhe Institute of Technology, Germany; 3Institute of Geological Sciences, University of Bern, Switzerland

Despite the extensive use of water as a coolant in nuclear reactors (both boiling and pressurized) as well as other industrial applications, the heterogeneous nucleate boiling mechanism controlling evaporation and condensation is still not sufficiently understood. This is particularly important within the fuel assembly systems, where the boiling on the surface leads to inefficient heat transfer and increased thermal fatigue.

A recent molecular dynamics approach investigated the effect of different crystallographic orientations of zirconia (ZrO2) [1], the material used for the fuel cladding, identifying different contact angles for each. These results have been incorporated in a multiphase non-isothermal LB simulation, using a single-relaxation-time scheme to retrieve the momentum equation and a two-relaxation-time scheme for the energy equation [2].

The simulations investigate the behavior of vapour bubbles on and above rough zirconia surfaces, with emphasis on the effect of the contact angle. The generation of bubbles from small orifices, bubble coalescence and nucleation are investigated above rough surfaces. The results show a reduction of bubble waiting periods as the heating rate increases and faster bubble departure in hydrophilic surfaces. Initial simulations are conducted in 2D. For the acceleration of simulations in 3D, a parallel LB GPU code is being developed. Moreover, additional LB multiphase models are being incorporated.

1. Karalis, K., et al., Deciphering The Molecular Mechanism Of Water Boiling At Heterogeneous Interfaces. Scientific Reports, 2021. 11(19858).

2. Patel, R.A., et al., A three-dimensional lattice Boltzmann method based reactive transport model to simulate changes in cement paste microstructure due to calcium leaching. Construction and Building Materials, 2018. 166: p. 158-170.

4:40pm - 5:00pm

Comparison of Lattice Boltzmann Method Collision Operators for Simulation of Transient Thermal Conditions in Data Center

Sjölund, Johannes1,2; Summers, Jon1,2

1RISE Research Institutes of Sweden, Sweden; 2Luleå University of Technology, Sweden

This study evaluates three different lattice Boltzmann method-based (LBM) large-eddy simulations (LES) applied to thermal flow inside a data center. Thermal fields from the simulation are compared against time-series data recorded during operation of a real-world slab-floor data center containing 360 servers and thermal management using computer room air handling (CRAH) units.

The three LBM collision operators evaluated for velocity fields were single-relaxation time (SRT) Bhatnagar-Gross-Krook (BGK), two-relaxation time (TRT) both on a D3Q19 lattice, and multiple-relaxation time (MRT) on a D3Q27 lattice. The velocity fields were coupled to an SRT D3Q7 temperature field through advection and natural convection using Boussinesq approximation.

Good agreement between measured and simulated temperatures were seen in areas of low turbulence. The more complex operators were found to be more stable at higher Reynolds numbers and allow for greater fine-tuning of turbulence models. Although, in the present simulation differences in accuracy between them were minimal while computational performance was affected.

Date: Thursday, 30/June/2022
9:30am - 10:30amLBM and Complex Flows
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Michel Berthier, La Rochelle University
9:30am - 9:50am

Flow of plant protein doughs in extruder dies

van der Sman, Ruud

Wageningen University & Research, Netherlands, The

In this contribution we present a numerical model of the flow of plant protein dough through an extruder die, as occurs in the production of plant-based meat replacers. This model is to be coupled to another model describing the flow of the material in the extruder screw section. The combined model will be used for process design.

The protein dough is assumed to behave as a Herschel-Bulkley fluid, having a yield stress, and exhibiting shear thinning. These parameters have been measured as function of moisture content and temperature. It follows that the yield stress depends on Tg/T, the ratio of the (moisture dependent) glass transition temperature and the actual temperature. The shear thinning exponent is independent of temperature or moisture content.

The cooling die receives the protein dough at high temperatures in the range of 120-160$^oC$, and it will be cooled down to temperatures of 60-100$^oC$. The extruder will be operated at a constant throughput. The cooling of the dough in the die will involve a strong increase of the yield stress. Hence, in the middle of the flow channel an unyielded plug flow will develop. Shear rate gradients develop in a small boundary layer along the wall. Above all, we expect a lubrication layer will develop along the wall due to expulsion of moisture, leading to wall slip. Towards the end the plug flow will cover the entire cross section of the die.

Hence, for proper process design the flow model needs to be coupled to an energy balance solving the temperature profile within the extruder die. There will be a two-way coupling between the flow model and the energy balance: the dough rheology is strongly temperature dependent,

and the viscous dissipation can increase temperature.

The flow model is implemented using Lattice Boltzmann model, which has the advantage that shear stresses are directly locally available, and it can later be extended to multiphase flow, as plant protein doughs consists often of two different biopolymers. The issue of the singularity in the effective viscosity in the Herschel-Bulkley model is resolved via a biviscosity regularization. Wall slip will be modelled using the general formalism by Kalyon. A scaling analysis of the governing equations show that a 2D model will suffice for process design purposes.

The overall boundary condition is complex, which is governed by a constant throughput. The related flow profile is an unknown, and will develop over the length of the extruder die, due to the non-isothermal conditions. The required pressure gradient is the desired outcome of the simulation, and thus it can be prescribed directly. Hence, as a boundary condition we impose a pressure gradient, which will be varied such that the flow profiles in all cross sections matches that of the imposed throughput.

9:50am - 10:10am

Investigation of the Capture of Coarse Air-borne Particles at different Fibre Aspect Ratios using Lattice Boltzmann Method

Bhardwaj, Utsav1,2; Abraham, Jijo Derick1,2; Ray, Bahni1; Das, Dipayan1; Das, Apurba1; Mitchell, Travis2; Leonardi, Christopher2

1Indian Institute of Technology Delhi; 2The University of Queensland

Air pollution is one of the most burning and life-threatening global issues, for which the fibrous air filters have emerged extensively as a remedial solution. In the present study, the capture dynamics of coarse airborne particles and associated variation of filtration performance parameters (efficiency and pressure drop) with respect to the variations in aspect ratio of a single rectangular fibre have been investigated numerically in two dimensions. With the length scales corresponding to the fibre and particles being a few microns each, the mesoscopic method, viz. lattice Boltzmann method (LBM) has been used for simulations of airflow across the fibre. For simulations of the motion of particles and their capture by fibre under the influence of aerodynamic drag and gravity, the Lagrangian approach has been used. One-way coupling has been employed between the airflow and particles (where only airflow field determines the motion of particles), and the inter-particle interactions have not been considered as the concentration of particles is pretty small. In case of LBM, the D2Q9 lattice configuration has been used. Also, the single relaxation time model has been used to define the collision operator via BGK approximation. The fibre-air interface has been provided with no-slip boundary condition via bounce-back scheme whereas the upper and lower boundaries of the computational domain have been provided with either symmetry or free-slip boundary condition using specular reflection. The study presents the characteristic variations observed in the filtration performance parameters as the fibre aspect ratio is varied.

10:10am - 10:30am

Compressible lattice Boltzmann methods based on numerical collision

Thyagarajan, Karthik; Coreixas, Christophe; Latt, Jonas

University of Geneva/ Battelle, Switzerland

Over the past three decades, lattice Boltzmann methods (LBMs) have grown as serious alternatives to Navier-Stokes-Fourier (NSF) solvers for the simulation of isothermal and weakly compressible flows past realistic geometries. Nevertheless, most compressible LBMs available in the literature have difficulties to compete with NSF solvers due to an increased (1) size of the lattice required to get the correct macroscopic behavior, and/or (2) complexity of the numerical scheme to ensure stable simulations .

Recently, a GPU-accelerated and purely LB approach based on numerical equilibria was proposed as an efficient and accurate alternative. In this approach, equilibria are computed through a root-finding algorithm that imposes an arbitrary number of equilibrium moments, which alleviates common accuracy and stability limits encountered with relatively small lattices, polynomial equilibria and BGK collision model. Yet, the BGK approximation also leads to a number of physical and numerical limitations, e.g., fixed Prandtl number and stability issues.

In this talk, we propose to extend the numerical computation of equilibrium populations to their post-collision counterpart, hence, allowing for the direct control of diffusive fluxes through constraints on non-equilibrium moments. This idea was originally proposed in the context rarefied gas dynamics to impose the correct heat flux, and is further extended here to any non-equilibrium moment.

As a proof of concept, the D2Q37 lattice is adopted to study the effects of the numerical collision on both stability and accuracy. Particular attention is paid to the computation of gradients, which are used as constraints for non-equilibrium moments, and that can either be done locally (LB scheme) or thanks to a finite-difference scheme. The proposed approach can seamlessly run on CPUs or GPUs thanks to the recent upgrade of the C++ STL library and NVIDIA compiler. The numerical collision is tested for several benchmark problems of increasing complexity, and corresponding results provide a positive feedback to proceed further.

10:30am - 10:50amCoffee Break
10:50am - 11:50amMethod and Analysis II
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Li-Shi Luo, CSRC
10:50am - 11:10am

A consistent discrete divergence-free condition in lattice Boltzmann magnetohydrodynamics: a data-driven approach

Dellar, Paul

University of Oxford, United Kingdom

Magnetohydrodynamics combines the Navier-Stokes and Maxwell equations to describe the flow of electrically conducting fluids in magnetic fields. Maxwell’s equations require the magnetic field to evolve in a way that keeps the divergence of the magnetic field zero. This is analogous to the incompressibility condition for a fluid, except there is no analogue of a pressure in Maxwell’s equations.

Lattice Boltzmann magnetohydrodynamics relies upon kinetic representations of both the fluid and the electromagnetic field. There is an extra kinetic degree of freedom that represents the divergence of the magnetic field for slowly varying solutions, but its relation to any discrete approximation to the divergence of the magnetic field on the lattice has previously been mysterious.

We show empirically, using data from simulations, that there is an optimal finite difference stencil for approximating the discrete divergence of the magnetic field, with parameters that depend on the relaxation times for the different components of the kinetic representation of the electromagnetic field. We then show that the parameters for the optimal stencil can be derived analytically using operator algebra techniques, and that they resemble formulas for the optimal placement of no-slip boundaries between lattice points.

Finally, we show that adjusting the relaxation time for the kinetic degree of freedom mentioned above implements an extended magnetohydrodynamics with an extra scalar field to maintain the divergence-free condition. The joint evolution of this kinetic degree of freedom and the optimal finite difference approximation for the discrete divergence of the magnetic field matches analytical solutions of the extended magnetohydrodynamics equations.

11:10am - 11:30am

Conservative models for the compressible hybrid lattice Boltzmann method

Wissocq, Gauthier; Coratger, Thomas; Farag, Gabriel; Zhao, Song; Boivin, Pierre; Sagaut, Pierre

Aix-Marseille Université, France

A new methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum and energy equations are solved by different methods. It is here designed for developing new numerical discretizations of the total energy equation, adapted to a thermal coupling with the lattice Boltzmann method (LBM). The proposed methodology is based on a linear equivalence with standard discretizations of the entropy equation, which, as a characteristic variable of the Euler system, allows efficiently decoupling the energy equation with the LBM. To this extent, any LBM scheme is written under a finite-volume formulation involving fluxes, which are included in the total energy equation as numerical corrections. Three models are subsequently derived: a first-order upwind, a Lax-Wendroff and a MUSCL-Hancock schemes. They are assessed on standard academic test cases for compressible flows, with and without discontinuitities. Three key features are exhibited: 1) the models are conservative by construction, recovering correct jump relations across shock waves, 2) the stability and accuracy of entropy modes can be explicitly controlled, 3) the low dissipation of the LBM for isentropic phenomena is preserved.

11:30am - 11:50am

Limit consistency of lattice Boltzmann equations

Simonis, Stephan; Krause, Mathias J.

Karlsruhe Institute of Technology (KIT), Germany

We establish the notion of limit consistency as a novel technique to formally prove the consistency of lattice Boltzmann equations (LBE) to a given partial differential equation (PDE). For the purpose of illustration, the incompressible Navier–Stokes equations (NSE) are used as a paragon. Based upon the proven diffusion limit [L. Saint-Raymond (2003), doi: 10.1016/S0012-9593(03)00010-7] of the BGK Boltzmann equation (BGKBE) towards the NSE, we provide a successive discretization by nesting conventional Taylor expansions and finite differences. Tracking the discretization state of the domain for the particle distribution functions, we measure truncation errors at all levels within the derivation procedure. Via parametrizing equations and proving limit consistency of the resulting sequences, we retain the path towards the targeted PDE at each step of discretization, i.e. for the discrete velocity BGKBE (DVBGKBE) and the space-time discretized lattice BGKBE (LBGKBE). As a direct result, we unfold the discretization technique of lattice Boltzmann methods as chaining finite differences and provide a generic top-down derivation of the numerical scheme.

11:50am - 1:20pmLunch
Location: Room MSI 218, Maison des Sciences de l'Ingénieur (MSI), La Rochelle University
2:00pm - 10:00pmSocial Event & Gala Dinner
Location: Boat trip + Museum (corderie royale) + Gala Dinner
Date: Friday, 01/July/2022
8:30am - 9:30amInvited speaker
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Michel Berthier, La Rochelle University

From Langevin dynamics to kinetic Monte Carlo: the quasi-stationary distribution approach

Lelièvre, Tony

Ecole des Ponts ParisTech, France

We will present a mathematical framework to draw a rigorous connection between microscopic and mesoscopic models to describe the evolutions of materials at the atomistic scale: molecular dynamics, namely Langevin or overdamped Langevin dynamics, and kinetic Monte Carlo (a.k.a. Markov State Models), namely jump Markov processes with values in a discrete state space. This analysis is useful to analyze and justify numerical methods which use the jump Markov model underlying the molecular dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques à la D. Perez and A.F. Voter). It also provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.


- G. Di Gesù, T. Lelièvre, D. Le Peutrec and B. Nectoux, Sharp asymptotics of the first exit point density, Annals of PDE, 5(1), 2019.

- T. Lelièvre, Mathematical foundations of Accelerated Molecular Dynamics methods, In: W. Andreoni and S. Yip (Eds), Handbook of Materials Modeling, Springer, 2018.

- T. Lelièvre, M. Ramil and J. Reygner, Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence, Stochastic Processes and their Applications, 144, 176-201, (2022).

9:30am - 11:10amPhase-Field, Multiphase and Other Methods for Complex Fluids
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: François Dubois, CNAM & Univ. Paris-Saclay
9:30am - 10:30am

Three-phase contact implementations to progress towards rough-walled fractures

Mitchell, Travis Ryan1; Sashko, Dmytro1; Laniewski-Wollk, Lukasz1,2; Leonardi, Christopher1

1School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD4072, Australia; 2Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw00-665, Poland

The propagation of two-phase flows through complex geometries are ubiquitous in nature and have numerous application in engineering fields. Of particular interest in this work is the risk of migration of liquid and gas products adjacent to defective oil & gas wells, potentially causing leakage pathways to aquifers and or the surface. In this setting (i.e. defective cement), the flow geometries have a high degree of randomness generally forming complex microannular voids and fractures either through the wellbore cement or between the cement-formation and or cement-pipe boundaries. This work looks to describe these defects as fractures in which the surfaces are correlated self-affine random fields, which allows the random nature of fractures and cracks to be quantified based on a handful of measurable parameters. The aim is to investigate the dependence of relative permeability on these parameters.

In this work, the phase-field lattice Boltzmann model originally proposed by Fakhari et al. [1,2] is extended to account for three-phase contact angles using both the free-energy and geometric approaches for staircase and smoothly defined solid normals. These are often investigated in two-dimensional settings, with non-trivial extensions to complex, three-dimensional geometries. As such, a projection of the phase gradient on the fluid nodes to the plane tangent to the surface is proposed, simplifying the need to determine consistent normal vectors that correspond with the reference frame on every boundary node.

The existing implementations outlined in the literature along with various discretisation methods for the gradients are investigated. This is done through examining the performance and accuracy obtained when studying the Washburn law and interaction of droplets on curved boundaries. Finally, the methods are applied to a stochastically generated, three-dimensional fracture to show the variations in fluid behaviour that can be observed based on the implementation of the three-phase contact.

[1] Fakhari, A., Mitchell, T., Leonardi, C., Bolster, D., Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios, Physical Review E 96, 053301, 2017.

[2] Mitchell, T., Leonardi, C., Fakhari, A., Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios, International Journal of Multiphase Flow 107, 1-15, 2018.

10:30am - 10:50am

Engulfment of a drop on solids coated by thin and thick fluid films

Zhao, Chunheng

The City College of New York, United States of America

The short-time evolutions of water droplets propagating on both the thin and the thick oil films are explored by the conservative phase-field Lattice Boltzmann method (LBM). The simulation is conducted to investigate the effect of oil layer thickness on the spreading and the engulfing processes. The simulation and the mathematical derivation are used to demonstrate the scaling analysis of those processes. The simulation findings show that the spreading process on the thin film $H/R<<1$ follows the same scaling rule for both $Oh<<1$ and $Oh>>1$ at the short time: $r/R~ (T/t)^{0.5}$. Besides, 2D simulation produces a similar result comparing to 3D simulation for droplet spreading on thin film. When we increase the film thickness gradually, the effect of the film thickness on the spreading process disappears. This argument is also approved by the viscous dissipation from the flow field. Through the comparison between our simulation results and the experimental results, the short time spreading radius of $Oh<<1$ on a thick film follows the scaling rule: $r/R~(T/t_ \eta)^{0.6}$.

10:50am - 11:10am

Imposing Ratios of Outlet Flow Rates on Large Arterial Networks with Two-Element Windkessel Model: Parametric Analysis

Lo, Sharp Chim Yui1; McCullough, Jon1; Coveney, Peter V.1,2

1University College London, United Kingdom; 2University of Amsterdam, Netherlands

Substantial effort is being invested in the creation of a virtual human --- a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. However, no study to date has examined the conditions for this approach to hold in complex geometries. Here we clarify the general role of the resistance and capacitance in this approach. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4\% in a simple five-outlets model and 7\% in a human artery model comprising 10 outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.

11:10am - 11:30amCoffee Break
11:30am - 12:50pmLBM for MHD and Other Complex Flows
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Li-Shi Luo, CSRC
11:30am - 11:50am

The Role of Hydrodynamics in the Dynamic Response of Magnetic Particles in a Polymer Suspension

Kreissl, Patrick; Holm, Christian; Weeber, Rudolf

Institute for Computational Physics, University of Stuttgart, Germany

Composites of magnetic nanoparticles and polymers are interesting materials, as they combine viscoelastic properties of the polymers with the possibility for external control via a magnetic field. Possible applications include micro-actuation and drug delivery.

Many variants of such composite materials have been realized experimentally, spanning magnetic particles in polymer suspensions, hydrogels, and rubber-like materials. While those materials have been synthesized successfully, accessing microscopic detail experimentally is challenging. This is true in particular for the coupling between the magnetic nanoparticles and the polymers. For these questions, simulations are a very useful tool, as one can control the nanoparticle-polymer interaction and observe the corresponding dynamic response of the system.

In this contribution, we will focus on a model system consisting of magnetically blocked nanoparticles in a polymer suspension. The magnetic moment being blocked means that a re-alignment of the magnetic moment implies a rotation of the particle, and vice versa. This is a suitable approximation for cobalt ferrite nanoparticles with a size of several nanometers, as they are commonly used in experiments.

Magnetic AC susceptibility measurements, i.e., determining the magnetic response to a small applied AC magnetic field, are employed to probe the local environment of the magnetic particles[1]: assuming a Stokes-like friction of the particle, Germain-Dimarzio-Bishop theory can be used to calculate the local viscoelastic moduli as they are felt by the magnetic nanoparticles in their polymeric environment.

In our presentation, we will report on simulations corresponding to those experiments[2]. We use a combination of coarse-grained particles treated via molecular dynamics simulations coupled to a thermalized lattice-Boltzmann solver. By controlling the interactions between the nanoparticles and the polymers, we can determine the individual contributions to the magnetic susceptibility response, and hence the degree of mobility the particles possess in their local environment. Our results demonstrate that hydrodynamic interactions alone can reproduce the trends observed in experiments. Hydrodynamics therefore plays a key role in understanding magnetic particle-polymer coupling in those systems.

[1] E. Roeben, L. Roeder, S. Teusch, M. Effertz, U. Deiters, A. M. Schmidt. Colloid and Polymer Science, 292, 2014.

[2] P. Kreissl, C. Holm, R. Weeber. Soft Matter, 17, 2021.

11:50am - 12:10pm

Double MRT-LBM Analysis of the Coupled Radiation-Convection in a Square Cavity Filled with a Newtonian and non-Newtonian Hybrid Nanofluids under the magnetic field effects

chtaibi, khalid1,2; HASNAOUI, Mohammed1; Dahani, Youssef1; Ben Hamed, Haïkel2; Amahmid, Abdelkhalek1

1UCA, Faculty of Sciences Semlalia, Department of Physics, LMFE, B.P. 2390 Marrakesh, Morocco; 2UPJV, University Institute of Technology, LTI, Amiens, France

In recent decades, the Lattice Boltzmann Method (LBM) has become one of the most widely used numerical tools by the scientific community for simulating the heat transfer generated by natural convection of Newtonian and non-Newtonian fluids. The attractiveness of this mesoscopic method (simplicity, robustness and ease adaptation to different geometries) has facilitated its breakthrough and allowed it to compete seriously with the classical methods used for simulations purposes. In the present study, Double-Multiple-Relaxation-Time LBM was used to study heat transfer by MHD natural convection in a square configuration filled with a non-Newtonian Fe3O4-MWCNTs/water hybrid nanofluid in the presence of thermal radiation. The numerical simulation results were obtained at given Prandtl (Pr = 6.2) and Rayleigh (Ra = 105) numbers, while the remaining governing parameters were varied in wide ranges that are (0 ≤ Ha ≤ 50) for the Hartmann number, (0 ≤ φ ≤4%) for the nanoparticles volume fraction, (0.6 ≤ n ≤1.4) for the power-law index, and (0 ≤ Rd ≤ 2) for the radiation parameter. The findings of the present study illustrate the combining effects of these parameters in terms of streamlines, isotherms, and mean Nusselt numbers. Attenuation effects, characterized by a decrease in the flow intensity and a degradation of heat transfer process, are observed by increasing either the Hartmann number or the power-law index. However, increasing the radiation parameter or the nanoparticle volume fraction has led to an opposite effect that promotes both the heat transfer and the flow intensity.

12:10pm - 12:30pm

Non linear stability of Lattice Boltzmann scheme for under resolved simulation using global optimisation

Dubois, François1,2; Saint-Jean, Christophe3; Tekitek, Mohamed Mahdi3

1Laboratoire de Mathématiques d'Orsay, bâtiment 307, F-91405 Orsay, France; 2Conservatoire National des Arts et Métiers, LMSSC laboratory, F-75003 Paris, France; 3MIA laboratory, La Rochelle University, 17000 La Rochelle, France

Previous works [2,3] showed that D2Q9 BGK are unstable for test case given in [1] but D2Q9 MRT still stable for such nonlinear problem. In other hand, to investigate the stability of LB scheme, it is possible only numerically using von Neumann analysis [4], and only for linear case. In this work, the Minion et al. [1] test case stability is investigated for a fixed viscosity.

Regarding relaxation parameters(free, no effect up to order 2), the stability zone is investigated and characterized using a decision tree, a machine learning technique focused on interpretability. In order to go further, a simple global optimization method (genetic algorithm) is used to yield a set of stable relaxation parameters for the Minion et al. [1] and Taylor-Green test cases. Finally, we show that this optimization method also leads to find a stable non-trivial (non-physical) LB parameter set for the non-linear case.

[1] M.L. Minion, D.L. Brown, Performance of under-resolved two-dimensional incompressible flow simulations II, J. Comput. Phys., vol. 138, (1997).

[2] P.J. Dellar, Bulk and shear viscosities in lattice Boltzmann equations, Phys. Rev. E, 64 (2001).

[3] D. Ricot, Simon Marié, P. Sagaut, C. Bailly, Lattice Boltzmann method with selective viscosity filter, J. Comput. Phys., vol. 228, (2009).

[4] P. Lallemand, L.-S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, vol. 61, 2000

12:30pm - 12:50pm

Structure-preserving machine learning moment closure models for the radiative transfer equation

Huang, Juntao

Michigan State University, United States of America

In this talk, we present our work on structure-preserving machine learning (ML) moment closure models for the radiative transfer equation. Most of the existing ML closure models are not able to guarantee the stability, which directly causes blow up in the long-time simulations. In our work, with carefully designed neural network architectures, the ML closure model can guarantee the stability (or hyperbolicity). Moreover, other mathematical properties, such as physical characteristic speeds, are also discussed. Extensive benchmark tests show the good accuracy, long-time stability, and good generalizability of our ML closure model.

12:50pm - 1:20pmICMMES Awards & Closing
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Session Chair: Li-Shi Luo, CSRC
Session Chair: Catherine Choquet, La Rochelle University
1:20pm - 2:50pmLunch
Location: Room MSI 218, Maison des Sciences de l'Ingénieur (MSI), La Rochelle University

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