A lattice-Boltzmann inspired finite volume solver for compressible flows

Abstract

The lattice Boltzmann method (LBM) for compressible flow is characterized by good numerical stability and low dissipation, while the conventional finite volume solvers have intrinsic conversation and flexibility in using unstructured meshes for complex geometries. This paper proposes a strategy to combine the advantages of the two kinds of solvers by designing a finite volume solver to mimic the LBM algorithm. It assumes an ideal LBM that can recover all desired higher-order moments. Time-discretized moment equations with second-order temporal accuracy and physically consistent dissipation terms are derived from the ideal LBM. By solving the recovered moment equations, a finite volume solver that can be applied to nonuniform meshes naturally, enabling body-fitted mass-conserving simulations, is proposed. Numerical tests show that the proposed solver can achieve good numerical stability from subsonic to hypersonic flows, and low dissipation for a long-distance entropy spot convection. For the challenging direct simulations of acoustic waves, its dissipation can be significantly reduced compared with the Lax-Wendroff solver of the same second-order spatial and temporal accuracy, while only remaining higher than that of the LBM on coarse meshes. The analysis implies that approximations of third-order temporal accuracy are required to recover the low dissipation of LBM further.