Evaluation of an energy relaxation method for the simulation of unsteady, viscous, real gas flows

This study investigates a new energy relaxation method designed to capture the dynamics of unsteady, viscous, real gas flows governed by the compressible Navier-Stokes equations. We focus on real gas models accounting for inelastic molecular collisions and yielding temperature-dependent heat capacities. The relaxed Navier-Stokes equations are discretized using a mixed finite volume/finite element method and a high-order time integration scheme. The accuracy of the energy relaxation method is investigated on three test problems of increasing complexity: the advection of a periodic set of vortices, the interaction of a temperature spot with a weak shock, and finally, the interaction of a reflected shock with its trailing boundary layer in a shock tube. In all cases, the method is validated against benchmark solutions and the numerical errors resulting from both discretization and energy relaxation are assessed independently.