A sharp interface in-cell-reconstruction volume-of-fluid method for simulating compressible flows with immiscible interfaces

We present a hybrid tracking/capturing scheme using an in-cell-reconstruction technique (Smilijanovski, 1996) coupled to a volume-of-fluid volume tracking method, which is applicable to compressible flows that involve the interaction of shocks with phase interfaces. The proposed method maintains the phase interface as a sharp discontinuity within the continuum limit and avoids the need for small time steps by means of updating the volume averaged states of the cells. This is done by reconstructing the individual phase states from cell average values using the jump conditions across the phase interface and the geometric information provided by the volume-of-fluid method. The update to the volume averaged states is done by means of cell face aperature averaged updates resulting from pure-phase or mixed-face face regions. Effects of surface tension are incorporated directly into the individual phase states by the in-cell-reconstruction method and avoids errors due to discretization in typical surface tension modeling. The method also takes into account effects of viscosity and heat transfer due to heat conduction. A range of test cases is performed to demonstrate the robustness of the method.