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An accurate scheme for gas dynamical calculations

An accurate numerical method is developed for computing inviscid flows containing discontinuities. The method is based on flux vector splitting (FVS) and a third-order accurate upwind-biased compact finite-difference scheme. Two different flux splitting techniques, namely, the kinetic flux vector splitting (KFVS) and van Leer's flux splitting, are used to solve one-dimensional gas dynamics test problems. The idea of total variation diminishing (TVD) is employed to suppress spurious numerical oscillations. The stability and high-order accuracy of the scheme are shown.