Effects of Interface Regularization Models on Shock-Droplet Interactions

The dynamics of supersonic shock-droplet interactions are important in applications ranging from rotating detonation engines to hypersonic vehicle design. Studying these systems numerically is challenging as the interface between the liquid and surrounding gas must be tracked accurately and conservatively across a wide range of length scales, and different interface regularization techniques can dramatically affect the flow physics. In this work, four interface treatments are compared in the context of a canonical two-dimensional shock-droplet interaction: no regularization (Euler), the tangent-of-hyperbola interface capturing (THINC) reconstruction, and the conservative diffuse-interface (CDI) and accurate conservative diffuse-interface (ACDI) models. A compressible six-equation multiphase model is used to evolve the flow and all four are evaluated at shock Mach numbers $M_s = 2$ and $M_s = 3$. The effects of each technique are assessed qualitatively through droplet morphology and quantitatively through the liquid mass centroid trajectory and integral liquid-gas interface length, which together characterize bulk droplet motion and the development of small-scale interfacial structure. The simulations show that all four methods capture the early-time parent-droplet dynamics with broad agreement, but diverge substantially in the late-time wake structure, the degree of child-droplet development, and the total liquid-gas interface length. The Euler scheme produces continuously diffusing filamentary structures with no well-defined children, while THINC, CDI, and ACDI all produce distinct child droplets, but with morphological differences that depend on numerical parameters and Mach number. These results demonstrate that while bulk droplet translation is largely insensitive to the choice of interface treatment at early time, the resolved wake structure and droplet morphology are strongly model-dependent such that the choice of regularization mechanism and its parameters must be informed by the target observable in predictive simulations.