Investigation into the impact of interface thickness and Phase-Field modeling on interfacial instabilities in compressible multiphase flow

Excessive and non-uniform numerical diffusion poses challenges for accurate simulations of compressible interfacial flows with shocks using diffuse interface methods. Even with high-order accurate methods, material interfaces continually diffuse, thus making material regions ambiguous and deleteriously impacting wave propagation across interfaces. Further, the presence or absence of interfacial instabilities in canonical test problems appear to be highly dependent on initial conditions and schemes, with results varying substantially between methods for problems like the Kelvin-Helmholtz instability. In this work, we investigate the impact of interface thickness on interfacial instabilities and the interface topology for several flows, including the Kelvin-Helmholtz and Richtmyer-Meshkov instabilities, and a shock-bubble and shock-droplet interaction. Through the use of consistent and conservative Phase Fields, we are able to separate the modeling and numerical errors by maintaining uniform and constant thickness interfaces. We simulate several systems when the interface is free to diffuse and deform and when it is controlled by the Phase Field to observe the impact of interfacial thickness on the flow, and to observe the differences between the models with and without the Phase Field.