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**A rotationally biased upwind difference scheme for the Euler equations.**
*(English)*
Zbl 0557.76067

Summary: The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one-dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme is developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results are presented which illustrate the ability of this new method to resolve steady oblique shocks.

### MSC:

76L05 | Shock waves and blast waves in fluid mechanics |

76M99 | Basic methods in fluid mechanics |

76N15 | Gas dynamics (general theory) |

### Keywords:

angle between shock and computing grid; two-dimensional flows; upwind difference schemes; Euler equations; steady oblique shocks### Software:

HLLE
Full Text:
DOI

### References:

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