Explicit streamline diffusion finite element methods for the compressible Euler equations in conservation variables

Journal article, 1993

This paper concerns the streamline diffusion finite element method applied to one- and two-dimensional gas flow described by the inviscid Euler equations in conservation variables. We point out that the streamline diffusion method is a natural finite element analogue to upstream-type finite difference/volume schemes and in fact constitutes a general framework for a large class of them. We study explicit implementations of the method and derive different choices of stabilizing streamline diffusion matrices; in particular, we propose a consistent, fully multidimensional, version. A brief review of the theoretical background to the method is presented, and some numerical results in two dimensions are given.