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

HORACIO J. AGUERRE; SANTIAGO MÁRQUEZ DAMIÁN; JUAN M. GIMENEZ; NORBERTO M. NIGRO

JOURNAL OF COMPUTATIONAL PHYSICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2017 vol. 335 p. 21 - 49

0021-9991

This work presents a new and efficient strategy to handle non-conformal interfaces withthe aim of assuring the conservation of fluxes in Finite Volume problems. A conservativeinterpolation is developed for general transport equations. Due to the arbitrary connectivitybetween the interfaces, the interpolations require flux-based weights defining a complexnumerical stencil. In this context, a new method is proposed to simplify the coupling atthe interface based on the construction of a simplified supermesh. Here, a supermesh isnot completely defined, instead, the interface faces are logically duplicated (or multiplied)to generate a one-to-one connectivity between them. The simplified supermesh namedpseudo-supermesh eliminates the interpolations and assures the conservation of fluxesbased on the trivial connectivity. The area and the geometrical centroid of the new facesare redefined according to the overlapped sector of the original faces using the localsupermeshing approach. Since the arbitrary polygons resulting from the face intersectionsare not generated and introduced into the mesh, computational cost and implementationefforts are saved. The proposed method is tested focusing on the conservation of fluxes andon the accuracy, showing conservation to machine precision and second order convergenceas expected. In order to be able to solve large problems, the methodology is designed andimplemented to be run in parallel architectures showing an excellent efficiency.