An Implicit Algorithm for Finite Volume - Finite Element Coupling

We present an implicit coupling algorithm that is suitable for strongly coupled physical problems that were discretized by heterogeneous numerical schemes, namely finite volume and finite element methods. The primary characteristic of the proposed scheme is an implicit treatment of the heterogeneous schemes through a single matrix approach. The finite element and finite volume parts of the discretized domain exchange information through a coupling boundary and the resulting discretization coefficients are stored in a block matrix. The structure of the matrix is such that the coupling coefficients are stored in the off-diagonal blocks of the matrix, while finite element and finite volume subdomains are stored in the diagonal blocks of the matrix. A suite of efficient linear solvers based on the Krylov subspace methods were developed for the solution of the resulting coupling problem. Several demonstration cases that illustrate the coupling algorithm are presented.