Methods for the accurate computations of hypersonic flows. II: Shock-aligned grid technique.

*(English)*Zbl 1106.76422Summary: In order to eliminate or minimize the numerical error by shock waves due to grid distribution in multidimensional hypersonic flows, a new grid reconstruction scheme, the shock-aligned grid technique (SAGT), is proposed. The error due to shock waves in a non-shock-aligned grid system magnifies in proportion to the Mach number and propagates on the downstream side of the flow field to contaminate sensitive aerodynamic coefficients or flow quantities. SAGT, combined with the AUSMPW+ scheme proposed in Part I of the present work [Zbl 1106.76422], not only provides an accurate solution but also reduces the grid dependency of a numerical scheme without a substantial increase in computational cost. In addition, SAGT is robust and flexible enough to deal with complex flow problems involving shock interaction and reflection and equilibrium and nonequilibrium effects. Extensive numerical tests from a hypersonic blunt body flow to hypersonic nonequilibrium flows validate the accuracy, efficiency, robustness, and convergence characteristics of SAGT.

##### MSC:

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

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

65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of 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 |

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\textit{K. H. Kim} et al., J. Comput. Phys. 174, No. 1, 81--119 (2001; Zbl 1106.76422)

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