SHARP INTERFACE TERM FOR COMPRESSIBLE MULTIPHASE FLOW WITH SURFACE TENSION ON IRREGULAR GRIDS

Interface sharpening schemes take advantage of the fact that diffusion resulting from numerical discretization error of spatial PDEs acts like a Laplacian by adding an artificial counterbalancing negative diffusion term of the same form. In this paper an interface sharpening strength parameter is analytically derived at cell centers based on the local PDE transport characteristics and the cell geometry. The proposed interface sharpening scheme is applied to a compressible multiphase flow system of equations and is agnostic to the spatial distribution of cell centers in the mesh. Fluid equations of state are chosen to accurately capture interfacial dynamics between two fluids with a significant pressure difference since surrounding literature raises challenges of stabilizing high density contrasts. The relationship between (i) the magnitude of the standard deviation of the Gaussian convolution used to stabilize such field discontinuities across the interface and (ii) solution accuracy is discussed. The overall flow model is validated against various test cases to demonstrate effectiveness and accuracy. The proposed methods are implemented into Ablative Boundary Layers At The Exascale (ABLATE), an open-source software package being developed to simulate compressible multiphase flows.