Dissipative properties of Runge-Kutta schemes with upwind spatial approximation for the Euler equations
Abstract
We present in this paper how to construct a 4-stage Runge-Kutta method when the spatial approximation is a Muscl-type upwind scheme for the solution of the two-dimensional Euler equations. A theorical study is first conducted in the one-dimensional linear case, and then extended to the two-dimensional case where the equations are solved by multigrid techniques over unstructured finite element meshes. A few numerical experiments are presented, demonstrating the validity of the theoretical results.