A Six-Equation Multimaterial Method for Compact Finite Differences

High-order compact finite difference schemes' spectral-like accuracy is well suited for capturing turbulent mixing, but additional stabilization is needed to capture jumps in material properties in multimaterial flows. Localized artificial diffusivity (LAD) methods have been developed for compact finite differences to stabilize large material property jumps. However, the methods struggle to simulate stiff and complex equations of state due to an inability to enforce monotonic state variables with pressure/temperature equilibrium. We present a novel six-equation model for the compact finite difference method, which addresses these limitations by relaxing the pressure equilibrium requirement and explicitly tracking volume fractions and species energies. The strength of the proposed scheme is validated on a suite of test problems.