Abstract
Multi-dimensional upwind discretizations for the steady Euler equations are studied, with the emphasis on both a good accuracy and a good efficiency. The discretizations consist of a one-dimensional Riemann solver with locally rotated left and right cell face states, the rotation angle depending on the local flow solution. First, on the basis of a linear, scalar model equation, a study is made of the accuracy and stability properties of these schemes. Next the extension is made to the steady Euler equations. It is shown that for Euler flows, an appropriate local rotation angle can be found by maximizing a Riemann invariant along the middle subpath of the wave path in state space. For the steady, two-dimensional Euler equations, numerical results are presented for some supersonic test cases with either oblique contact discontinuity or oblique shock wave.
Note: This work was supported by the European Space Agency (ESA), through Avions Marcel Dassault — Bréguet Aviation (AMD-BA).
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© 1992 Springer Fachmedien Wiesbaden
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Koren, B., Hemker, P.W. (1992). Multi-D Upwinding and Multigridding for Steady Euler Flow Computations. In: Vos, J.B., Rizzi, A., Ryhming, I.L. (eds) Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 35. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13974-4_9
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DOI: https://doi.org/10.1007/978-3-663-13974-4_9
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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