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| A robust HLLC scheme and stability analysis |
| Received:February 10, 2020 Revised:July 10, 2020 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20200210001 |
| KeyWord:hypersonic flow HLLC scheme carbuncle phenomenon entropy wave viscosity shear wave viscosity shock instability |
| Author | Institution |
| 胡立军 |
衡阳师范学院 数学与统计学院, 衡阳 |
| 袁海专 |
湘潭大学 数学与计算科学学院, 湘潭 |
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| Abstract: |
| Godunov-type numerical methods that can accurately capture contact wave and shear wave,such as the popular HLLC scheme,will cause shock anomalies when used in simulating hypersonic flow problems.The stability analysis of HLLC scheme shows that all perturbations in the flow direction are damped,but the perturbations of density and shear velocity in the transverse direction are undamped.The 2D Sedov blast wave problem with special symmetry demonstrates the close relationship between transverse flux and instability.The pressure ratio and Mach number are used to detect the transverse interfaces in the subsonic region of numerical shock layer,and a shock stable HLLC scheme is proposed by adding the viscosity of entropy wave and shear wave to numerical fluxes at these interfaces.The analysis shows that all perturbations in the transverse direction are damped with the help of viscosity of entropy wave and shear wave.A series of numerical tests show that the new scheme can not only successfully suppress all kinds of shock anomalies,but also retain the merit of low dissipation of the original HLLC scheme. |