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Solution of the Riemann problem of classical gasdynamics. (English) Zbl 1236.76054
Summary: The mere structure of the linearly degenerate characteristic field of the equations of gas dynamics provides the natural frame to build the exact Riemann solver for any gas satisfying the condition $$e_{vvv}(s,v)\neq 0$$, which guarantees the genuine nonlinearity of the acoustic modes. Differently from single equation methods rooted in the $$\gamma$$-law ideal gas assumption, the new approach is based on the system of two nonlinear equations imposing the equality of pressure and of velocity, assuming as unknowns the two values of the specific volume, or temperature, on the two sides of the contact discontinuity. Newton iterative method is used. The resulting exact solver is implemented for van der Waals gas, including the treatment of nonpolytropic behavior with molecular vibrations at thermal equilibrium, as well as for Martin–Hou gas, as an example of the general applicability of the proposed approach. The correctness of the new Riemann solver is demonstrated by comparisons with other numerical techniques.

MSC:
 76N15 Gas dynamics, general 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 76M20 Finite difference methods applied to problems in fluid mechanics
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