EXPLICIT STREAMLINE DIFFUSION FINITE-ELEMENT METHODS FOR THE COMPRESSIBLE EULER EQUATIONS IN CONSERVATION VARIABLES

The 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. © 1993 Academic Press, Inc.