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Two-dimensional Riemann solver for Euler equations of gas dynamics. (English) Zbl 1043.76042
Authors’ summary: We construct a Riemann solver based on two-dimensional linear wave contributions to the numerical flux that generalizes the one-dimensional Roe method. The solver is based on a multistate Riemann problem and is suitable for arbitrary triangular grids or any other finite volume tessellations of the plane. We present numerical examples illustrating the performance of the method, using both first- and second-order accurate numerical solutions. The numerical flux contributions are due to one-dimensional waves and multidimensional waves originating from the corners of the computational cell. Under appropriate CFL restrictions, the contributions of one-dimensional waves dominate the flux, which explains good performance of dimensionally split solvers in practice. The multidimensional flux corrections increase the accuracy and stability, allowing a larger time step. The improvements are more pronounced on a coarse mesh and for large CFL numbers. For the second-order method, the improvements can be comparable to the improvements resulting from a less diffusive limiter.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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