An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes

Abstract

In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge–Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge–Kutta scheme and nonuniform meshes of present lattice Boltzmann method are discussed through simulations of a two-dimensional lid-driven cavity flow on nonuniform meshes. Moreover, the comparison simulations of the present method and multiple relaxation time lattice Boltzmann subgrid method are conducted qualitatively and quantitatively.