A Finite Element–Finite Volume Code Coupling for Optimal Control Problems in Fluid Heat Transfer for Incompressible Navier–Stokes Equations

Samuele Baldini, Giacomo Barbi, Giorgio Bornia, Antonio Cervone, Federico Giangolini, Sandro Manservisi () and Lucia Sirotti
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Samuele Baldini: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Giacomo Barbi: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Giorgio Bornia: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Antonio Cervone: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Federico Giangolini: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Sandro Manservisi: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Lucia Sirotti: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy

Mathematics, 2025, vol. 13, issue 11, 1-29

Abstract: In this work, we present a numerical approach for solving optimal control problems for fluid heat transfer applications with a mixed optimality system: an FEM code to solve the adjoint solution over a precise restricted admissible solution set and an open-source well-known code for solving the state problem defined over a different one. In this way, we are able to decouple the optimality system and use well-established and validated numerical tools for the physical modeling. 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 code. 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.

Keywords: Boussinesq approximation; conjugate heat transfer; natural convection; optimal control; code coupling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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