Year: 2026
Type: article
Abstract: The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions for multi-dimensional vectorial lattice Boltzmann schemes tackling systems of hyperbolic conservation laws. In the scalar case, we prove convergence for schemes with monotone relaxation to the weak entropy solution by Bardos, Leroux, and Nédelec [Comm. Partial Differential Equations 4 (1979), pp. 1017–1034], following the path by Crandall and Majda [Math. Comp. 34, (1980), pp. 1–21]. Numerical experiments are conducted both for scalar and vectorial problems, and demonstrate the effectiveness of equilibrium boundary conditions in capturing significant physical phenomena.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4173
Authors: Denise Aregba-Driollet, Thomas Bellotti
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414835349
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