An efficient hybrid method for solving Euler equations. (English) Zbl 1433.65167
The authors present a hybrid method for solving Euler equations compatible with high-order schemes. A seventh-order WENO scheme is used for spatial reconstruction. The method combines a simple MUSCL-type flux method and a characteristic flux approach. In the MUSCL-type flux approach, the inviscid fluxes are computed, using approximate Riemann solvers HLL and HLLC schemes based on the WENO-reconstructed state variables. In critical regions where VF (variable-based flux) may produce spurious oscillations, a novel, low-dissipation HLL-based CF (characteristic flux) approach is applied. The VF/CF hybrid method is shown to produce high-resolution, essentially non-oscillatory results for a number of 1D and 2D problems at a fraction of the cost of a pure CF approach. The results highlight the relation between Kelvin-Helmholtz roll-ups and numerical instabilities along slip lines.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35Q31 | Euler equations |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 76L05 | Shock waves and blast waves in fluid mechanics |
Keywords:
Euler equations; hybrid method; high-order WENO schemes; characteristic fluxes; shock sensorReferences:
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