A Direct Implicit Discretization Approach for Arbitrary Non-conformal Interface by Using a Virtual Cell

Abstract

A direct implicit discretization approach is presented for an arbitrary non-conformal interface by using a virtual cell on unstructured meshes. In this study, the virtual cell is supposed to be located at the neighbour of a target cell adjacent to the non-conformal interface. Any computational value on a virtual cell is formulated as a linear combination of values on contribution cells, which are determined by the nearest neighbouring cells or surface intersecting cells. The linear formulation simplifies the process of implementing implicit discretization for the governing equations. The approach is simple and efficient for information transfer through the interface because it avoids mesh stitching or iterations based on explicit discretization for treating topologically inconsistent meshes. Several numerical tests verify that the proposed method is capable and efficient for dealing with the arbitrary non-conformal interface.