Numerical analysis of compressible two-phase flows using cartesian cut-cell method

We have developed a sharp interface method for treating contact discontinuities of compressible multi-phase fluids using 3-D Cartesian cut-cell grids. The location of evolving discontinuities in the Cartesian grid is captured implicitly by the level set method. The intersections between the 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 of velocity, temperature, stress and energy across phase interfaces are satisfied 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 for the reconstruction with jump conditions and Laplace law test show the validity and accuracy of the proposed sharp interface method for two-phase fluids.