Lattice Boltzmann methods for some 2-D nonlinear diffusion equations:Computational results

Technical Report · Mon Jan 01 00:00:00 EST 1990

DOI:https://doi.org/10.2172/6226434· OSTI ID:6226434

Elton, B H; Rodrigue, G H ^[1]; Levermore, C D ^[2]

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1. California Univ., Davis, CA (USA). Dept. of Applied Science Lawrence Livermore National Lab., CA (USA)
2. Arizona Univ., Tucson, AZ (USA). Dept. of Mathematics

In this paper we examine two lattice Boltzmann methods (that are a derivative of lattice gas methods) for computing solutions to two two-dimensional nonlinear diffusion equations of the form {partial derivative}/{partial derivative}t u = v ({partial derivative}/{partial derivative}x D(u){partial derivative}/{partial derivative}x u + {partial derivative}/{partial derivative}y D(u){partial derivative}/{partial derivative}y u), where u = u({rvec x},t), {rvec x} {element of} R{sup 2}, v is a constant, and D(u) is a nonlinear term that arises from a Chapman-Enskog asymptotic expansion. In particular, we provide computational evidence supporting recent results showing that the methods are second order convergent (in the L{sub 1}-norm), conservative, conditionally monotone finite difference methods. Solutions computed via the lattice Boltzmann methods are compared with those computed by other explicit, second order, conservative, monotone finite difference methods. Results are reported for both the L{sub 1}- and L{sub {infinity}}-norms.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: DOE/DP; National Science Foundation (NSF)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6226434
• Report Number(s): UCRL-JC-104691; ON: DE91004175; CNN: DMS-8914420
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
PARTIAL DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTION
ASYMPTOTIC SOLUTIONS
BOLTZMANN STATISTICS
CHAPMAN-ENSKOG THEORY
DIFFUSION
FINITE DIFFERENCE METHOD
NONLINEAR PROBLEMS
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
990200* - Mathematics & Computers