Conservative interpolation on surface interfaces for transport problems in the Finite Volume Method

Abstract

This paper presents a new strategy to couple non-matching interfaces in the Finite Volume Method based on a conservative interpolation. In contrast to most of the conservative methods, the current approach does not modify the mesh and therefore, the connection between variables at both sides of the interfaces is solved using interpolation. The conservation of fluxes is imposed by a pair of vector equations which relates the matrix coefficients of the Finite Volume problem with the weighting factors used for interpolating. These relations are satisfied by projecting the matrix coefficients from an interface to its opposite and then computing the weighting factors according to a conservation principle. This new strategy is implemented for an incompressible flow solver including a transport equation of a scalar function. The conservation and accuracy properties of the proposed methodology are analyzed in a set of numerical problems where the theory and the computational implementation are validated.