Robustness of the hybrid DRP-WENO scheme for shock flow computations

This paper describes a new variant of hybrid scheme that is constructed by a wave-capturing scheme and a nonoscillatory scheme for flow computations in the presence of shocks. The improved fifth-order upwind weighted essentially nonoscillatory scheme is chosen to be conjugated with the seven-point dispersion-relation-preserving scheme by means of an adaptive switch function of grid-point type. The new hybrid scheme can achieve a better resolution than the hybrid scheme which is based on the classical weighted essentially scheme. Ami Harten's multiresolution analysis algorithm is applied to density field for detecting discontinuities and setting point values of the switch function adaptively. Moreover, the tenth-order central filter is applied in smooth part of the flow field for damping dispersion errors. This scheme can promote overall computational efficiency and yield oscillation-free results in shock flows. The resolution properties and robustness of the new hybrid scheme are tested in both 1D and 2D linear and nonlinear cases. It performs well for computing flow problems with rich structures of weak/strong shocks and large/small vortices, such as the shock-boundary layer interaction problem in a shock tube, which illustrates that it is very robust and accurate for direct numerical simulation of gas-dynamics flows. Copyright (c) 2011 John Wiley & Sons, Ltd.