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| A genuinely multidimensional Riemann solver based on WENO reconstruction |
| Received:May 31, 2022 Revised:July 12, 2022 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20220531002 |
| KeyWord:Riemann solver genuinely multidimensional WENO reconstruction flux splitting shock instability |
| Author | Institution |
| 胡立军 |
衡阳师范学院 数学与统计学院, 衡阳 |
| 谭诗德 |
湘潭大学 数学与计算科学学院, 湘潭 |
| 袁海专 |
湘潭大学 数学与计算科学学院, 湘潭 |
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| Abstract: |
| The finite volume scheme plays an important role in numerical computation of fluid dynamics due to its good conservation and mesh adaptability.Numerical determination of fluxes is the key to implement the finite volume method.In one-dimensional cases,the theory of obtaining fluxes by solving the local Riemann problem has been relatively mature.However,when solving multidimensional problems,the traditional dimension splitting method only considers the information propagating along the direction normal to the interface,which not only affects the accuracy but also may cause numerical instability and thus induce the unphysical phenomenon.A genuinely multidimensional Riemann solver based on the convection-pressure flux splitting method is constructed,and the multidimensional property is achieved by solving multidimensional Riemann problems at vertices of the grid.The high-order accuracy in space is achieved by implementing the fifth-order WENO reconstruction and the third-order TVD Runge-Kutta scheme for time discretization.Results of a series of numerical experiments show that the genuinely multidimensional Riemann solver not only has a higher resolution but also can effectively overcome the numerical instability in calculations of multidimensional strong shock waves. |