An adaptive interface sharpening methodology for compressible multiphase flows

A numerical methodology is developed to combine the advantages of adaptive mesh refinement (AMR) and interface sharpening technique. A five-equation compressible multiphase model with capillary and viscous effects is considered. The solver employs a wave propagation method along with the Tangent of Hyperbola for INterface Capturing (THINC) scheme. To calculate interface normal and curvature, an implicit filtering method is introduced which transforms the sharpened volume fraction variable to a variant with smoothed distribution. The accuracy and performance of our method is assessed through its application to multiple compressible interface problems ranging from high-Mach number shock-interface interaction to gravity driven flows with viscosity and surface tension effects. The results obtained for one-dimensional shock-tube and tin-air interaction problems are shown to compare well with analytical data. The flow patterns predicted for shock-bubble interaction and under-water explosion match those from the landmark experimental and numerical studies. Furthermore, the trends and values predicted for spike position in the Rayleigh-Taylor instability and bubble's center location in bubble rising are consistent with those found in literature. Particularly, it is shown that the coupled AMR-THINC method remarkably prevents excessive interface smearing and captures delicate interfacial features such as shear-induced instabilities encountered in shock-bubble interaction.