Abstract: Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
This work is concerned with constructing a robust, high-order approximation of the compressible Euler equations for gas dynamics supplemented with an arbitrary or tabulated equation of state. In particular, we show how to construct a high-order graph-viscosity coefficient using an interpolated entropy pair useful when the equation of state is given by tabulated experimental data. Similarly, we construct an entropy surrogate functional that is used in a convex limiting technique that preserves the invariant domain of the system. Finally, the numerical method is then verified with analytical solutions and then validated with several benchmarks seen in the literature and laboratory experiments.