http://worldcat.org/entity/work/id/30340675

The P¹-RKDG method for two-dimensional Euler equations of gas dynamics

Earlier work is continued on a class on nonlinearly stable Runge Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws. Two dimensional Euler equations for gas dynamics are solved using p1 elements. We discuss the generalization of the local projection, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions. Numerical examples include the standard regular shock reflection problem, the forward facing step problem and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of our approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods. Generalizations to pk elements with k equal to or greater than the use of adaptive triangulations to minimize local errors constitute ongoing research.

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