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

Technical Report ·
DOI:https://doi.org/10.2172/6226434· OSTI ID:6226434
;  [1];  [2]
  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., CA (USA)
Sponsoring Organization:
DOE/DP; 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