WENO Scheme-based Lattice Boltzmann Flux Solver For Simulation Of Compressible Flows

Lattice Boltzmann flux solver is based on the kinetic molecular theory. It removes the shortages of traditional lattice Boltzmann method(LBM) such as limitation to viscous flows and uniform mesh. But it only has two order ac-curacy, and it exists oscillations at the neighborhood of stagnation point in simulating hypersonic flows. In order to overcome the drawback, we present, a WENO scheme-based lattice Boltzmann flux solver for simulation of compress-ible flows(WENO-LBFS). Traditional FD-WENO scheme is a finite difference weighed essentially non-oscillatory scheme. It has many features including high-accuracy, high-resolution, robustness and small amount of calculation. WENO scheme-based lattice Boltzmann flux solver combines the advantages of WENO scheme and lattice Boltzmann flux solver, thus it is destined to be a high-order accuracy, high-resolution and robust numerical scheme to capture shock waves.Combining WENO scheme and viscous lattice Boltzmann flux solver(LBFS ?), we present viscous WENO-LBFS ?. Due to large numerical viscosity, viscous LBFS ? can effectively capture shock waves, but it may damage smooth solution. So viscous WENO-LBFS ? its an effective scheme to solve compressible problems with complex shock waves. By the results of two-dimensional problem, Lax prob-lem, Woodward-Colella problem, double Mach reflection problem and implosion problem, comparing the results computed by WENO scheme based on traditional fluxes, we validate the accuracy and efficiency of viscous WENO-LBFS ?.On the basis of existing viscous WENO-LBFS ?, we present inviscid WENO-LBFS ? and hybrid WENO-LBFS ?. Inviscid WENO-LBFS ? can accurately solve smooth problem. Hybrid WENO-LBFS ? combines the advantages of in-viscid WENO-LBFS ? and viscous WENO-LBFS ?. Improving viscous WENO-LBFS ?, it can not only effectively capture strong shock waves, but it can ac-curately calculate the solution of smooth region. In the meanwhile, We present a hybrid WENO-LBFS ?. Different from hybrid WENO-LBFS ?, in which governing function is determined by the biggest governing function of two sides of neighboring control volume at the cell, the governing function in the hybrid WENO-LBFS IV is the maximum value of the governing function of all the neighboring control volume at the cell. By two-dimensional problem, Riemann problem, Woodward-Colella problem and a mach 3 wind tunnel with a step, we validate the accuracy and efficiency of hybrid WENO-LBFS ? and hybrid WENO-LBFS ?.