Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
---|---|---|
Page(s) | 1935 - 1958 | |
DOI | https://doi.org/10.1051/m2an/2024058 | |
Published online | 10 October 2024 |
Convergence of Lattice Boltzmann methods with overrelaxation for a nonlinear conservation law
Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, 33400 Talence, France
* Corresponding author: denise.aregba@math.u-bordeaux.fr
Received:
6
February
2024
Accepted:
11
July
2024
We approximate a nonlinear multidimensional conservation law by Lattice Boltzmann Methods (LBM), based on underlying BGK type systems with finite number of velocities discretized by a transport-collision scheme. The collision part involves a relaxation parameter w which value greatly influences the stability and accuracy of the method, as noted by many authors. In this article we clarify the relationship between w and the parameters of the kinetic model and we highlight some new monotonicity properties which allow us to extend the previously obtained stability and convergence results. Numerical experiments are performed.
Mathematics Subject Classification: 65M12 / 35L60 / 65M08
Key words: Lattice Boltzmann method / nonlinear conservation laws / convergence
© The authors. Published by EDP Sciences, SMAI 2024
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