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

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 two-stage 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 in space. It is shown that the previous finite-difference lattice Boltzmann method (FDLBM) (Guo and Zhao, 2003) 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 other high order FDLBMs, this two T2S2-FDLBMs keep the simplicity of standard lattice Boltzmann method. Compared with the previous FDLBM and lattice Boltzmann method, the two T2S2-FDLBMs are 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.