Adaptive Cartesian sharp interface method for three-dimensional multi-phase flows

We have developed a sharp interface method for treating interfacial discontinuities of compressible multi-phase fluids on 3-D Cartesian cut-cell grids. The evolution of the interfacial discontinuities in Cartesian grid is captured by level set method. The intersections between interfacial fronts and Cartesian grids are interpolated using level set function information at vertices of Cartesian grids. Triangular surfaces are then constructed on the interfacial fronts. A novel cell merging method is used for complex topological changes. Jump conditions across discontinuous interfaces are enforced by reconstruction of interfacial flow variables using constrained least squares method. Inviscid flux across internal faces of the same fluid is calculated by local Lax Friedrichs (LLF) flux. Validation results show the validity and accuracy of the proposed sharp interface method for two-phase fluids.