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

We present a hybrid capturing/tracking method for finite volume solvers of compressible flows involving two immiscible fluids that are described by equations of states for ideal gases. The approach is an extension of the two-dimensional level set based in-cell-reconstruction method originally proposed by Smiljanovski et al. [1] for deflagration waves to three-dimensional flows involving interfaces between two immiscible fluids with surface tension forces. The interface motion is captured by an extension to the conservative, un-split geometric volume-of-fluid technique of Owkes and Desjardins [2]. The resulting method is a sharp interface method that avoids time-step restrictions or merging/mixing rules due to cut-cells by using cell-face-aperture averaged waves to update the volume averaged states of cells containing the interface directly. The method furthermore avoids the use of any mixed states in discretization stencils, by reconstructing the pure fluid states in each mixed cell, explicitly enforcing the jump conditions across the interface. Simulations of compressible flows that involve the interaction of shocks with interfaces between immiscible fluids are performed to demonstrate the performance of the proposed method.