Conference Agenda

SC3: Short Courses 3
Monday, 27/June/2022:
1:45pm - 3:00pm

Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University

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

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.