Analyses and reconstruction of the lattice Boltzmann flux solver

Abstract

The lattice Boltzmann flux solver (LBFS) uses the finite volume method (FVM) to update macroscopic variables while uses the local solution of lattice Boltzmann equation (LBE) to calculate fluxes at the cell interface. It overcomes the intrinsic drawbacks of the lattice Boltzmann method which include the limitation of uniform mesh, coupled time interval with mesh spacing, and extra memory requirement. The recovered macroscopic equations indicate that LBFS is a weakly compressible model. In general, directly solving weakly compressible models with the central difference scheme suffers numerical instability and additional treatments are needed to stabilize computation. The present paper firstly recovers the macroscopic equations of LBFS (MEs-LBFS) with actual numerical dissipative terms by approximating its actual computational process and then analyzes the mechanisms of the good performance of LBFS. Based on these mechanisms, the reconstructed LBFS (RLBFS), which directly uses macroscopic variables rather than LBE to calculate fluxes at the cell interface, is proposed. Numerical tests indicate that RLBFS preserves the mechanisms of restraining pressure oscillation and stabilizing numerical computation in LBFS perfectly. It is capable of simulating both steady and unsteady, 2D and 3D, viscous and inviscid flows as well, and has higher computational efficiency than LBFS.