A finite-difference lattice Boltzmann model with second-order accuracy of time and space for incompressible flow

TL;DR

This paper introduces a second-order accurate finite-difference lattice Boltzmann model for incompressible flow, improving stability and accuracy over previous methods through a novel discretization scheme.

Contribution

The paper presents a new T2S2-FDLBM with second-order accuracy in time and space, including a simplified time discretization and stability analysis, extending prior models.

Findings

More accurate than previous FDLBM and SLBM

Enhanced stability with CFL number up to 0.9

Effective for simulating incompressible flows on non-uniform grids

Abstract

In this paper, a kind of finite-difference lattice Boltzmann method with the second-order accuracy of time and space (T2S2-FDLBM) is proposed. In this method, a new simplified two-stage fourth order time-accurate discretization approach is applied to construct time marching scheme, and the spatial gradient operator is discretized by a mixed difference scheme to maintain a second-order accuracy both in time and space. It is shown that the previous finite-difference lattice Boltzmann method (FDLBM) proposed by Guo [1] is a special case of the T2S2-FDLBM. Through the von Neumann analysis, the stability of the method is analyzed and two specific T2S2-FDLBMs are discussed. The two T2S2-FDLBMs are applied to simulate some incompressible flows with the non-uniform grids. Compared with the previous FDLBM and SLBM, the T2S2-FDLBM is more accurate and more stable. The value of the Courant-Friedrichs-Lewy condition number in our method can be up to 0.9, which also significantly improves the computational efficiency.