Methods for the accurate computations of hypersonic flows. I: AUSMPW+scheme.

*(English)*Zbl 1106.76421Summary: In order to overcome some difficulties observed in the computation of hypersonic flows, a robust, accurate and efficient numerical scheme based on AUSM-type splitting is developed. Typical symptoms appearing in the application of AUSM-type schemes for high-speed flows, such as pressure wiggles near a wall and overshoots across a strong shock, are cured by introducing weighting functions based on pressure (AUSMPW). A newly improved version of the AUSMPW scheme, called AUSMPW+, is developed to increase the accuracy and computational efficiency of AUSMPW in capturing an oblique shock without compromising robustness. With a new definition of the numerical speed of sound at a cell interface, capturing an oblique shock is remarkably enhanced, and it can be proved that an unphysical expansion shock is completely excluded. With simple Mach number interpolation functions, AUSMPW+ is efficient to implement. Extensive numerical tests from supersonic frozen flows to hypersonic nonequilibrium flows validate that the AUSMPW+ scheme provides accurate solutions for the computation of high-speed flows.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

76K05 | Hypersonic flows |

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

76V05 | Reaction effects in flows |

##### Keywords:

oblique shock; accuracy; robustness; efficiency; hypersonic flows; equilibrium gas; nonequilibrium gas
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\textit{K. H. Kim} et al., J. Comput. Phys. 174, No. 1, 38--80 (2001; Zbl 1106.76421)

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