2006/05/23 by R. A. Brownlee, Alexander N. Gorban, A. N. Gorban +2 · 2 citations
Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Lattice Boltzmann Simulation Studies #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.74.037703
published as Phys Rev E 74 (2006), 037703 · 4 pages, 9 figures
arxiv created 2006/05/23 · openalex publication_date 2006/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The lattice Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modeling complex fluid flow. However, it is acknowledged that the method can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We propose a simple technique to stabilize the LBM by monitoring the difference between microscopic and macroscopic entropy. Populations are returned to their equilibrium states if a threshold value is exceeded. We coin the name Ehrenfests' steps for this procedure in homage to the vehicle that we use to introduce the procedure, namely, the Ehrenfests' coarse-graining idea.