A Genuinely Multidimensional Riemann Solver Based on the TV Splitting

HU Li-jun; YUAN Li

doi:10.21656/1000-0887.370207

Volume 38 Issue 3

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HU Li-jun, YUAN Li. A Genuinely Multidimensional Riemann Solver Based on the TV Splitting[J]. Applied Mathematics and Mechanics, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207

Citation:

HU Li-jun, YUAN Li. A Genuinely Multidimensional Riemann Solver Based on the TV Splitting[J]. Applied Mathematics and Mechanics, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207

Citation:

HU Li-jun, YUAN Li. A Genuinely Multidimensional Riemann Solver Based on the TV Splitting[J]. Applied Mathematics and Mechanics, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207

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A Genuinely Multidimensional Riemann Solver Based on the TV Splitting

doi: 10.21656/1000-0887.370207

HU Li-jun,
YUAN Li

State Key Laboratory of Scientific and Engineering Computing; Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R.China

Funds: The National Basic Research Program of China(973 Program)(2010CB731505); The National Natural Science Foundation of China(11321061)

Received Date: 2016-07-04
Rev Recd Date: 2016-08-11
Publish Date: 2017-03-15

Abstract

Abstract

A genuinely multidimensional HLL Riemann solver was given. The flux vector of the Euler equations was split into convection and pressure parts based on the TV splitting method. The convection part was evaluated by means of the upwind method similar to the AUSM scheme, and the pressure part was evaluated with a modified HLL scheme. In the modified HLL scheme, the choices of wave speed were based on the pressure system rather than the Euler equations, and the pressure difference was replaced by the density difference in the dissipative term in order to capture the contact accurately. To obtain the genuinely multidimensional property, the numerical fluxes at the midpoint and the 2 corners of the cell interface were evaluated respectively, and the Simpson rule was used to obtain the final numerical flux through the interface. The linear reconstruction based on the SDWLS gradients was implemented for 2nd-order spatial accuracy, and the time derivative was discretized with the 2nd-order Runge-Kutta method. Compared with the traditional 1D HLL scheme, the genuinely multidimensional HLL scheme can effectively capture the contact discontinuity, and use larger time steps. Unlike other schemes which can capture the contact discontinuity accurately such as the HLLC scheme, the genuinely multidimensional HLL scheme eliminates the phenomena of numerical shock instability in 2D cases.
- Euler equation,
- TV splitting,
- corner flux,
- multidimensional Riemann solver,
- contact capturing,
- numerical shock instability

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References(43)

References

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