Solution of the Riemann problem of classical gasdynamics

The mere structure of the linearly degenerate characteristic field of the equations of gasdynamics provides the natural frame to build the exact Riemann solver for any gas satisfying the condition evvv(s,v)≠0, which guarantees the genuine nonlinearity of the acoustic modes. Differently from single equation methods rooted in the γ-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.