We consider an adaptive multiresolution-based lattice Boltzmann scheme, which we have recently introduced and studied from the perspective of the error control and the theory of the equivalent equations. This numerical strategy leads to high compression rates, error control and its high accuracy has been explained on uniform and dynamically adaptive grids. However, one key issue with non-uniform meshes within the framework of lattice Boltzmann schemes is to properly handle acoustic waves passing through a level jump of the grid. It usually yields spurious effects, in particular reflected waves. In this paper, we propose a simple mono-dimensional test-case for the linear wave equation with a fixed adapted mesh characterized by a potentially large level jump. We investigate this configuration with our original strategy and prove that we can handle and control the amplitude of the reflected wave, which is of fourth order in the space step of the finest mesh. Numerical illustrations show that the proposed strategy outperforms the existing methods in the literature and allow to assess the ability of the method to handle the mesh jump properly.
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@article{CRMATH_2022__360_G7_761_0,
author = {Bellotti, Thomas and Gouarin, Lo{\"\i}c and Graille, Benjamin and Massot, Marc},
title = {Does the multiresolution lattice {Boltzmann} method allow to deal with waves passing through mesh jumps?},
journal = {Comptes Rendus. Math\'ematique},
pages = {761--769},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
number = {G7},
year = {2022},
doi = {10.5802/crmath.319},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/crmath.319/}
}
TY - JOUR AU - Bellotti, Thomas AU - Gouarin, Loïc AU - Graille, Benjamin AU - Massot, Marc TI - Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps? JO - Comptes Rendus. Mathématique PY - 2022 SP - 761 EP - 769 VL - 360 IS - G7 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.319/ DO - 10.5802/crmath.319 LA - en ID - CRMATH_2022__360_G7_761_0 ER -
%0 Journal Article %A Bellotti, Thomas %A Gouarin, Loïc %A Graille, Benjamin %A Massot, Marc %T Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps? %J Comptes Rendus. Mathématique %D 2022 %P 761-769 %V 360 %N G7 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.319/ %R 10.5802/crmath.319 %G en %F CRMATH_2022__360_G7_761_0
Bellotti, Thomas; Gouarin, Loïc; Graille, Benjamin; Massot, Marc. Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps?. Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 761-769. doi : 10.5802/crmath.319. http://archive.numdam.org/articles/10.5802/crmath.319/
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