Linear lattice Boltzmann flux solver for simulating acoustic propagation

Abstract

A linear lattice Boltzmann flux solver (LLBFS) is developed based on the high-precision finite-volume method (FVM) and is used to simulate problems involving acoustic propagation. The least-squares-based finite difference (LSFD) is used to construct the high-precision FVM, which discretizes the linear Navier–Stokes equations (LNSE). In terms of the flux calculation for the interface of the control cell, the LLBFS is derived by comparing the macroscopic and microscopic variables through the Chapman–Enskog (C-E) multi-scale analysis, which establishes the relationship between the linear lattice Boltzmann equation (LBE) and the LNSE. The algorithm has the following advantages. First, the proposed LLBFS inherits the advantages of the lattice Boltzmann flux solver (LBFS), i.e., the local solution of the lattice Boltzmann equation is used to calculate the fluxes; handling the inviscid and viscous fluxes simultaneously makes for a more consistent algorithm and it can be expanded to the multi-dimensional scheme without approximation. Second, solving the LNSE using the high-precision FVM on unstructured grids, which enables problems involving acoustic waves interacting with complex geometries can be simulated conveniently. To validate the accuracy and robustness of the proposed method, several cases are simulated, including acoustic waves propagating in an inviscid and viscous mean flow and interacting with complex geometries.