A Finite Element-Finite Volume Code Coupling for Optimal Control Problems in Fluid Heat Transfer

In this work we present a numerical approach for solving optimal control problems for fluid heat transfer applications with an emphasis on the coupling of multiple codes. Specifically, two different CFD codes, OpenFOAM (finite volume based) and FEMuS (finite element based), have been used to solve the optimality system, while the data transfer between them is managed by the external library MEDCOUPLING. The state equations are solved in the finite volume code, while the adjoint and the control are solved in the finite element one. Two examples taken from the literature are implemented in order to validate the numerical algorithm: the first one considers a natural convection cavity resulting from a Rayleigh-Bénard configuration, and the second one is a Conjugate Heat Transfer problem between a fluid and a solid region.