Lattice Boltzmann model approximated with finite difference expressions

TL;DR

This paper introduces a modified lattice Boltzmann method using finite difference approximations to improve the accuracy of fluid property simulations, validated through various flow tests.

Contribution

It proposes a new FD-LBM scheme that replaces first-order terms with finite differences and adds nonlinear terms, enhancing the traditional lattice Boltzmann approach.

Findings

FD-LBM scheme performs well in shear wave, Stokes, and Poiseuille flow tests

Compared favorably with traditional lattice Boltzmann methods in accuracy

Demonstrates improved approximation of fluid properties

Abstract

We show that the asymptotic properties of the link-wise artificial compressibility method are not compatible with a correct approximation of fluid properties. We propose to adapt the previous method through a framework suggested by the Taylor expansion method and to replace first order terms in the expansion by appropriate three or five points finite differences and to add non linear terms. The "FD-LBM" scheme obtained by this method is tested in two dimensions for shear wave, Stokes modes and Poiseuille flow. The results are compared with the usual lattice Boltzmann method in the framework of multiple relaxation times.