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 highcflnumbers (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, and a shock–bubble interaction. The method shows very sharp resolution of shocks.