A numerical theory of lattice gas and lattice Boltzmann methods in the computation of solutions to nonlinear advective-diffusive systems

Technical Report · Mon Sep 24 00:00:00 EDT 1990

DOI:https://doi.org/10.2172/6480937· OSTI ID:6480937

Elton, A B.H.

A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: DOE/DP
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6480937
• Report Number(s): UCRL-LR-105090; ON: DE91002566
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ADVECTION
NONLINEAR PROBLEMS
DIFFUSION
BOLTZMANN STATISTICS
CHAPMAN-ENSKOG THEORY
CONVERGENCE
EIGENVALUES
EIGENVECTORS
FINITE DIFFERENCE METHOD
NAVIER-STOKES EQUATIONS
NUMERICAL ANALYSIS
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MASS TRANSFER
MATHEMATICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
656001* - Condensed Matter Physics- Solid-State Plasma
990200 - Mathematics & Computers
640400 - Fluid Physics