Real gas computation using an energy relaxation method and high-order WENOschemes

In this paper, we use a recently developed energy relaxation theory by Coqu el and Perthame and high order weighted essentially nonoscillatory (WENO) s chemes to simulate the Euler equations of real gas. The main idea is an ene rgy decomposition under the form epsilon = epsilon(1) + epsilon(2), where e psilon(1) is associated with a simpler pressure law (gamma-law in this pape r) and the nonlinear deviation epsilon(2) is convected with the flow. A rel axation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(1) gamma-law. The algorithm only calls for the original pre ssure law once per grid point per time step, without the need to compute it s derivatives or any Riemann solvers. Both one- and two-dimensional numeric al examples are shown to illustrate the effectiveness of this approach. (C) 1999 Academic Press.