Solution of the Riemann problem forvan der Waals gas

The mere structure of the linearly degenerate eigenmode of the equations of gasdynamics provides a quite natural frame to build a new exact Riemann solver for a gas endowed with arbitrary thermodynamic properties. 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, with unknowns the two values of specific volume (or temperature) on the two sides of the contact discontinuity. Newton iterative method is used and the resulting solver is implemented in the case of the van der Waals gas, including the treatment of nonpolytropic behaviour at thermal equilibrium. The correctness of the proposed algorithm is demonstrated by comparisons with other numerical techniques.