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

AGUERRE, HORACIO J.; MÁRQUEZ DAMIÁN, SANTIAGO; NIGRO, NORBERTO M.

JOURNAL OF COMPUTATIONAL PHYSICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2019 vol. 395 p. 144 - 165

0021-9991

This paper presents a new strategy to couple non-matching interfaces in the Finite VolumeMethod based on a conservative interpolation. In contrast to most of the conservativemethods, the current approach does not modify the mesh and therefore, the connectionbetween variables at both sides of the interfaces is solved using interpolation. Theconservation of fluxes is imposed by a pair of vector equations which relates the matrixcoefficients 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 itsopposite and then computing the weighting factors according to a conservation principle.This new strategy is implemented for an incompressible flow solver including a transportequation of a scalar function. The conservation and accuracy properties of the proposedmethodology are analyzed in a set of numerical problems where the theory and thecomputational implementation are validated.