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On Godunov-type methods for gas dynamics. (English) Zbl 0642.76088
We describe a new approximate Riemann solver for compressible gas flow. In contrast to previous Riemann solvers, where a numerical approximation for the pressure and the velocity at the contact discontinuity is computed, we derive a numerical approximation for the largest and smallest signal velocity in the Riemann problem. Having obtained the numerical signal velocities, we use theoretical results by A. Harten [e.g.: J. Comput. Phys. 49, 357-393 (1983; Zbl 0565.65050)] to obtain the full approximation. A stability condition for the numerical signal velocities is derived. We also demonstrate a relation between the signal velocities and the dissipation contained in the corresponding Godunov-type method. The computation of signal velocities for a general (convex) equation of state is discussed. Numerical results for the one- and two-dimensional compressible gas dynamics equations are also given.

76N15 Gas dynamics (general theory)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L67 Shocks and singularities for hyperbolic equations
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