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In this paper, a kind of finite-difference lattice Boltzmann method with thesecond-order accuracy of time and space (T2S2-FDLBM) is proposed. In thismethod, a new simplified two-stage fourth order time-accurate discretizationapproach is applied to construct time marching scheme, and the spatial gradientoperator is discretized by a mixed difference scheme to maintain a second-orderaccuracy both in time and space. It is shown that the previousfinite-difference lattice Boltzmann method (FDLBM) proposed by Guo [1] is aspecial case of the T2S2-FDLBM. Through the von Neumann analysis, the stabilityof the method is analyzed and two specific T2S2-FDLBMs are discussed. The twoT2S2-FDLBMs are applied to simulate some incompressible flows with thenon-uniform grids. Compared with the previous FDLBM and SLBM, the T2S2-FDLBM ismore accurate and more stable. The value of the Courant-Friedrichs-Lewycondition number in our method can be up to 0.9, which also significantlyimproves the computational efficiency.

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