ID 310

An in-cell-reconstruction volume-of-fluid method for simulating flows of compressible immiscible fluids

 

Abstract:

We present an improvement over the 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 (Kannan, 2017). The proposed method uses a second-order wave propagation algorithm by Leveque (2010) and avoids the need for small time steps by using cell face aperature averaged wave updates of the volume averaged states of cells containing the phase interface. The resulting method is a sharp interface method that maintains the phase interface as a discontinuity in the continuum limit. 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 current advancements allow for the use of a stiffened equation-of-state, characteristic of highly stiffened two-phase systems. The interaction of the propagated waves with the interface in a given cell is taken into account by incorporating an exact two-phase Riemann solver following Kamm (2015). A range of test cases is performed to demonstrate the robustness of the method.