A preconditioned lattice Boltzmann flux solver for steady flows on unstructured hexahedral grids

Abstract

The lattice Boltzmann flux solver (LBFS), first introduced by Shu et al. (2014) on structured meshes, allows fluid flow problems to be solved on unstructured meshes discretised by the finite volume method. The solver calculates the macroscopic fluxes at the cell interfaces from a local reconstruction of the lattice Boltzmann solution. In this paper the LBFS is extended to three-dimensional unstructured hexahedral meshes and a preconditioned lattice Boltzmann flux solver (PLBFS) is presented. The PLBFS involves applying the preconditioning technique proposed by Guo (2004) to the LBFS and is achieved by modifying the equilibrium distribution function used to calculate the macroscopic fluxes at the cell interface. When the PLBFS is applied to steady flow problems, it is shown that convergence is significantly accelerated and the accuracy of predictions with unstructured grids is greatly improved when compared to the LBFS. This paper also introduces a strategy for choosing the optimal value of preconditioning factor with unstructured hexahedral meshes.