Extension of High-Order Lattice Boltzmann Flux Solver for Simulation of Three-Dimensional Compressible Flows

Abstract

In this paper, a high-order lattice Boltzmann flux solver (LBFS) based on flux reconstruction (FR) is presented for simulating the three-dimensional compressible flows. Unlike the original LBFS employing finite volume methods, the current method (FR-LBFS) can achieve arbitrary high-order accuracy with a compact stencil. High-order schemes based on finite volume methods often compromise parallel efficiency and complicate boundary treatment. In contrast, LBFS incorporates physical effects in calculating inviscid fluxes, providing superior shock-capturing capabilities over traditional approximate Riemann solvers. The present method combines the strengths of both FR and LBFS, yielding enhanced performance. Specifically, there is limited analysis of compact high-order LBFS in simulations of three-dimensional compressible flows. Several benchmark test cases are employed to validate the superiority of the current method, and the results show good agreement with established literature values. The shock tube problem and inviscid Taylor-Green vortex demonstrate the shock-capturing capability and low-dissipation characteristics of FR-LBFS. Meanwhile, the decaying homogeneous isotropic turbulent flow and the flow around a triangular airfoil highlight the accuracy of the current method in turbulence simulation. The obtained numerical results demonstrate that the proposed method holds considerable promise for applications in simulations of compressible and turbulent flows.