2007/03/31 by R. A. Brownlee, Alexander N. Gorban, A. N. Gorban +2 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Generative Adversarial Networks and Image Synthesis #Lattice Boltzmann Simulation Studies #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2007.09.031
published as Physica A, V. 387, Issues 2-3 (2008), Pages 385-406 · 30 pages, 9 figures, 1 table
arxiv created 2007/03/31 · openalex publication_date 2007/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity - nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy "trimming") and (ii) based on filtering of nonequilibrium entropy (entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate estimate of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100*100 grid. All limiter constructions are applicable for both entropic and non-entropic quasiequilibria.