Lattice Boltzmann Model Based on the Rebuilding-Divergency Method for the Laplace Equation and the Poisson Equation

Authors:
Huimin Wang;Guangwu Yan;Bo Yan
Affiliations:
College of Mathematics, Jilin University, Changchun, P.R. China 130012 and College of Applied Mathematics, Jilin University of Finance and Economics, Changchun, P.R. China 130117;College of Mathematics, Jilin University, Changchun, P.R. China 130012;College of Mathematics, Jilin University, Changchun, P.R. China 130012
Venue:
Journal of Scientific Computing
Year:
2011

Citing 6
Cited 2

Nonlinear Stability of Compressible Thermal Lattice BGK Models

SIAM Journal on Scientific Computing
A Lattice Boltzmann equation for waves

Journal of Computational Physics
Lattice Bhatnagar—Gross—Krook model for the Lorenz attractor

Physica D
Accelerated Lattice Boltzmann Schemes for Steady-State Flow Simulations

Journal of Scientific Computing
Three-dimensional multi-relaxation time (MRT) lattice-Boltzmann models for multiphase flow

Journal of Computational Physics
Steady state convergence acceleration of the generalized lattice Boltzmann equation with forcing term through preconditioning

Journal of Computational Physics

Numerical Method Based on the Lattice Boltzmann Model for the Kuramoto-Sivashinsky Equation

Journal of Scientific Computing
A Lattice Boltzmann Model for the Reaction-Diffusion Equations with Higher-Order Accuracy

Journal of Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, a new lattice Boltzmann model based on the rebuilding-divergency method for the Poisson equation is proposed. In order to translate the Poisson equation into a conservation law equation, the source term and diffusion term are changed into divergence forms. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher-order moments of equilibrium distribution functions are obtained. Thus, by rebuilding the divergence of the source and diffusion terms, the Laplace equation and the Poisson equation with the second accuracy of the truncation errors are recovered. In the numerical examples, we compare the numerical results of this scheme with those obtained by other classical method for the Green-Taylor vortex flow, numerical results agree well with the classical ones.