Conservative handling of arbitrary non-conformal interfaces using an efficient supermesh

Abstract

This work presents a new and efficient strategy to handle non-conformal interfaces with the aim of assuring the conservation of fluxes in Finite Volume problems. A conservative interpolation is developed for general transport equations. Due to the arbitrary connectivity between the interfaces, the interpolations require flux-based weights defining a complex numerical stencil. In this context, a new method is proposed to simplify the coupling at the interface based on the construction of a simplified supermesh. Here, a supermesh is not completely defined, instead, the interface faces are logically duplicated (or multiplied) to generate a one-to-one connectivity between them. The simplified supermesh named pseudo-supermesh eliminates the interpolations and assures the conservation of fluxes based on the trivial connectivity. The area and the geometrical centroid of the new faces are redefined according to the overlapped sector of the original faces using the local supermeshing approach. Since the arbitrary polygons resulting from the face intersections are not generated and introduced into the mesh, computational cost and implementation efforts are saved. The proposed method is tested focusing on the conservation of fluxes and on the accuracy, showing conservation to machine precision and second order convergence as expected. In order to be able to solve large problems, the methodology is designed and implemented to be run in parallel architectures showing an excellent efficiency.