Improving pressure equilibrium preservation in conservative simulations of compressible real-fluid interfacial flows using a high-order formulation

We present a high-order accurate and fully conservative numerical scheme for simulating compressible, multi-species, and real-fluid interfacial flows. This study focuses on improving the preservation of pressure equilibrium (PE) at fluid interfaces. The key to achieving high-order PE preservation is the modification of the internal energy flux by incorporating both the divergence form and the product-rule form of the thermodynamic Jacobian. Simulations of multi-species and real-fluid advection demonstrate that the proposed fourth- and sixth-order schemes significantly improve PE preservation compared to a previously proposed second-order scheme.