An Unconditionally Stable Method for the Euler Equations

. We discuss how to combine a front tracking method with dimensional splitting to solve systems of conservation laws numerically in two space dimensions. In addition we present an adaptive grid refinement strategy. The method is unconditionally stable and allows for moderately high cfl numbers (typically 1--4), and thus it is highly efficient. The method is applied to the Euler equations of gas dynamics. In particular, it is tested on an expanding circular gas front, a wind tunnel with a step, a double Mach reflection as well as a shock-bubble interaction. The method shows very sharp resolution of shocks. 1. Introduction Front tracking has proved to be an efficient tool to analyze hyperbolic conservation laws rigorously, both scalar equations and systems, in one space dimension. We demonstrate how to use front tracking for systems of conservation laws as an unconditionally stable numerical method in two space dimensions, and we test it on the Euler equations of gas dynamics. Let us fi..