Development of accurate and robust genuinely two-dimensional HLL-type Riemann solver for compressible flows. (English) Zbl 1521.76426
Summary: When using the conventional direction splitting method to calculate multidimensional high speed gasdynamical flows, Riemann solvers capable of resolving contact surface and shear wave accurately will suffer from different forms of shock instability, such as the notorious carbuncle phenomenon. The stability analysis shows that the lack of dissipation in the direction transverse to the shock front leads to the shock instability of low-dissipation HLLEM solver. To overcome this defect, an accurate and carbuncle-free genuinely two-dimensional HLL-type Riemann solver is proposed. Using Zha-Bilgen splitting method, the flux vector of two-dimensional Euler equations is split into the convective flux and pressure flux. An algorithm similar to AUSM+ scheme is adopted to calculate the convective flux and the pressure flux is calculated by the low-dissipation HLLEM scheme. Following Balsara’s idea, the genuinely two-dimensional properties of the new solver are achieved by solving the two-dimensional Riemann problem that considers transversal features of the flow at each vertex of the cell interface. Numerical results of benchmark tests demonstrate that the new solver has higher resolution and better robustness than the conventional HLLEM solver implemented in dimension by dimension.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 76N15 | Gas dynamics (general theory) |
Keywords:
Euler equations; HLL-type Riemann solver; genuinely two-dimensional; Zha-Bilgen splitting; carbuncle phenomenon; shock instabilityReferences:
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