Conference Agenda

LBM for MHD and Other Complex Flows
Friday, 01/July/2022:
11:30am - 12:50pm

Session Chair: Li-Shi Luo, CSRC
Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University

Pôle Communication Multimédia Reseaux, La Rochelle University, 44 Avenue Albert Einstein, La Rochelle.

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.