Convergence of Convective–Diffusive Lattice Boltzmann Methods
Copyright policy )Convergence of Convective–Diffusive Lattice Boltzmann Methods
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.
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
- Lawrence Berkeley National Laboratory United States
- University of Arizona United States
- Fujitsu (Japan) Japan
- University of California, Davis United States
Cellular Automata and Lattice Gases (nlin.CG), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Kinetic theory of gases in time-dependent statistical mechanics, Initial value problems for nonlinear first-order PDEs, FOS: Physical sciences, convective-diffusive lattice Boltzmann methods, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Nonlinear Sciences - Cellular Automata and Lattice Gases, monotone lattice Boltzmann methods
Cellular Automata and Lattice Gases (nlin.CG), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Kinetic theory of gases in time-dependent statistical mechanics, Initial value problems for nonlinear first-order PDEs, FOS: Physical sciences, convective-diffusive lattice Boltzmann methods, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Nonlinear Sciences - Cellular Automata and Lattice Gases, monotone lattice Boltzmann methods
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