Second-order force scheme for lattice Boltzmann method

TL;DR

This paper derives a second-order force scheme for the lattice Boltzmann method using kinetic theory, improving accuracy by eliminating lattice effects through higher-order discretization, and verifies it numerically for advanced collision models.

Contribution

It introduces a second-order force scheme for lattice Boltzmann methods based on kinetic theory, applicable to various collision models including SMRT.

Findings

The force scheme is derived analytically from kinetic theory.

Lattice effects are eliminated with second-order discretization.

Numerical verification confirms the scheme's effectiveness.

Abstract

We present an a priori derivation of the force scheme for lattice Boltzmann method based on kinetic theoretical formulation. We show that the discrete lattice effect, previously eliminated a posteriori in BGK collision model, is due to first-order space-time discretization and can be eliminated generically for a wide range of collision models with second-order space-time discretization. Particularly, the force scheme for the recently developed spectral multiple-relaxation-time (SMRT) collision model is obtained and numerically verified.