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High Resolution Relaxed Upwind Schemes in Gas Dynamics

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Abstract

Numerical schemes based on relaxation are typically central difference schemes. In the case of supersonic flows, however, central differences are unphysical approximations. Introducing a shift in the relaxation approximation relaxed upwind schemes are constructed. Similar as central relaxed schemes, the new upwind versions also avoid the nonlinear Riemann problem and staggered grids. In addition, they simulate the physical domain of dependence correctly even in transonic flow regimes. The performance of the methods is illustrated by an acoustic shock interaction in gas dynamics.

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  1. Numerical Analysis, Lund University, Box 118, SE-221 00, Lund, Sweden

    H. Joachim Schroll

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  1. H. Joachim Schroll
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Schroll, H.J. High Resolution Relaxed Upwind Schemes in Gas Dynamics. Journal of Scientific Computing 17, 599–607 (2002). https://doi.org/10.1023/A:1015174730877

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