WENO Scheme-Based Lattice Boltzmann Flux Solver for Simulation of Compressible Flows

In this paper, the finite difference weighed essentially non-oscillatory (WENO) scheme is incorporated into the recently developed lattice Boltzmann flux solver (LBFS) to simulate compressible flows. The resultant WENO-LBFS scheme combines advantages of WENO scheme and LBFS, e.g., high-order accuracy, high resolution and physical robustness. Various numerical tests are carried out to compare the performance of WENO-LBFS and that of other WENO-based flux solvers, including the Lax-Friedrichs flux, the modification of the Harten-Lax-van Leer flux, the multi-stage predictor-corrector flux and the flux limiter centered flux. It turns out that WENO-LBFS is able to capture discontinuous profile in shock waves. Comparatively, the WENO-LBFS scheme costs less CPU time and eases programming.