An approximate linearised Riemann solver for the Euler equations for real gases (Q1095749)

The linearised approximate Riemann solver of \textit{P. L. Roe} was proposed in 1981 for the solution of the Euler equations of gas dynamics where the properties of the fluid are represented by the ideal equation of state [J. Comput. Phys. 43, 357-372 (1981; Zbl 0474.65066)]. We seek here to extend this scheme to the solution of the Euler equations in one dimension for real gases. At each stage we shall as far as possible draw a parallel with Roe's scheme for the ideal equation of state. Results for the extended scheme are presented for a particular problem of shock reflection for three different equations of state. In Section 2 we look at the Jacobian matrix of the flux function for the Euler equations with a general convex equation of state, and in Section 3 derive an approximate Riemann solver for the solution of these equations. In Section 4 we give some particular examples of nonideal equations of state, and in Section 5 we describe a standard test problem involving shock reflection. Finally, in Section 6 we display the numerical results achieved for this test problem with three different equations of state.