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| A simple Riemann solver accurate for contact discontinuity |
| Received:April 25, 2021 Revised:September 21, 2021 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20210425001 |
| KeyWord:compressible flow contact-capturing Rusanov scheme HLLC scheme hyperbolic tangent function robustness |
| Author | Institution |
| 胡立军 |
衡阳师范学院 数学与统计学院, 衡阳 |
| 杜玉龙 |
北京航空航天大学 数学科学学院, 北京 |
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| Abstract: |
| The finite volume method based on Godunov-type numerical scheme is the mainstream method for solving hyperbolic conservation law systems and the performance of the numerical scheme is largely determined by the Riemann solver for calculating the numerical flux at the cell interface.The one-wave Rusanov solver and the two-wave HLL solver have the advantages of simplicity,high efficiency and good robustness,but they are too dissipative in resolving the contact discontinuity.The complete-wave HLLC scheme can capture contact discontinuities accurately,but its applications in high Mach number flow problems are limited by the shock instability phenomenon. In this paper,the hyperbolic tangent function and the fifth-order WENO scheme are used to reconstruct the density values on both sides of the cell interface and the boundary variation diminishing algorithm is used to reduce the density difference in the dissipative term of Rusanov scheme,so as to improve the resolution for contact discontinuity significantly.Results of a series of numerical experiments demonstrate that compared with the complete-wave HLLC solver,the proposed Riemann solver has not only higher resolution but also better shock stability. |