A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

In this paper, a high-order scheme based on the lattice Boltzmann flux solver (LBFS) is proposed to simulate viscous compressible flows. The flux reconstruction (FR) approach is adopted to implement the spatial discretization. The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables. Meanwhile, a switch function is used in LBFS to adjust the magnitude of the numerical viscosity. Thus, it is more beneficial to capture both strong shock waves and thin boundary layers. Moreover, the viscous flux is computed according to the local discontinuous Galerkin method. Some typical compressible viscous problems, including manufactured solution case, lid-driven cavity flow, supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil, are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.