Three dimensional cut-cell Cartesian method for interfacial discontinuity of multi-phase fluids

We have developed a 3-D Cartesian cut-cell method for sharp treatment of contact discontinuities of multi-phase fluids. 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. Quadratic Surface recovery was conducted to the triangulated surfaces for accurate calculation of geometric features of the front surfaces. A novel cell merging method is proposed for complex topological changes. For the validation of the level set solver on adaptive Cartesian grids, the solver was applied to standard sample problems. The switching approach to the 5^th order WENO and 2^nd order central differencing gave satisfactory results in solution accuracy and flexibility for unstructured Cartesian grids. Some numerical results of grid-convergence tests on accuracy of surface recovery were also presented. For cubic interpolation, the order of accuracy of vertex coordinate is 4^th order and surface curvature is 2^nd order accurate, which is deemed to be required for the multiphase flow solution since the surface tension force should be calculated as accurately as the other terms in the flow equations. Preliminary results of cell merging are also shown.