The Riemann Problem for the Euler Equations with Nonconvex and Nonsmooth Equation of State: Construction of Wave Curves

The Riemann problem is considered for the investigation of nonclassical wave phenomena in Bethe--Zel'dovich--Thompson (BZT)-fluids and fluids which undergo a phase transition, i.e., the isentropes suffer kinks at the saturation boundaries. These fluids are modeled by a general equation of state that also takes into account regions of negative nonlinearity where the isentropes are nonconvex in the pressure-volume plane. Here the physical model is based on thermodynamical equilibrium. Both nonsmoothness as well as nonconvexity significantly influence the composition of the wave curves which are crucial for determining the solution for the Riemann problem for the Euler equations. This work gives explicit criteria for the composition of these wave curves by elementary wave types such as shocks, simple waves, and composite waves. Numerous examples for different wave curve compositions are presented.