A geometric-based sharp-interface approach for simulations of compressible multiphase flows

Sharp-interface methods for compressible multiphase flows have the desirable property of not introducing a length scale that artificially characterizes the numerically thickened interface, resulting in a significant reduction in mesh resolution requirements for large-scale simulations. The present method is developed based on the ghost fluid method (GFM), cf. Fedkiw et al., JCP, 1999. The formulation permits discontinuities as the solution of the governing partial differential equations in the weak form, allowing the physical interfacial conditions to be explicitly imposed without numerical regularization. Instead of the level-set function used in GFM and its variants, a color function has been designed to track the evolution of the interface topology, and a geometric interface reconstruction approach is developed using computer graphics theory. The reconstruction enables a more accurate evaluation of the local interface normal and curvature without incurring excessive computational cost. The results of the numerical calculations, such as the interaction of shock waves and phase interfaces, have shown the effectiveness and enhancements in capturing complex interfacial phenomena with relatively coarse mesh resolutions. The grid convergence study indicates that the present formulation of the sharp-interface approach distinctively defines the resolvable and subgrid scales, which in turn supports rigorous formulations of closure modules in multiphase turbulent flow simulations.