1993/05/25 by Bracy H. Elton, Garry Rodrigue, Garry H. Rodrigue +4
Computer Science · Engineering · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Generative Adversarial Networks and Image Synthesis #Lattice Boltzmann Simulation Studies #comp-gas #nlin.CG
paper · pdf · doi:10.48550/arxiv.comp-gas/9305002
39 pages; LaTeX and PsFig; 400kb uuencoded/compressed/tarred PostScript figures; submitted to the SIAM Journal on Numerical Analysis. AMS(MOS) subject classifications 35F25, 65M06, 65M12, 76R99, 82C40
arxiv created 1993/05/25 · openalex publication_date 1993/05/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence, consistency, and stability are defined through truncated Hilbert expansions. In this setting it is shown that consistency and stability imply convergence. Monotone lattice Boltzmann methods are defined and shown to be stable, hence convergent when consistent. Examples of diffusive and convective-diffusive lattice Boltzmann methods that are both consistent and monotone are presented.