IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i2p238-d1565220.html
   My bibliography  Save this article

Optimal Control of Heat Equation by Coupling FVM and FEM Codes

Author

Listed:
  • Samuele Baldini

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Giacomo Barbi

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Antonio Cervone

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Federico Giangolini

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Sandro Manservisi

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Lucia Sirotti

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite volume OpenFOAM code and the adjoint-control equation using a variational formulation of the problem with the in-house finite element FEMuS code. The variational formulation of the problem is the natural framework for accurately capturing the control correction while OpenFOAM guarantees the accuracy of the state solution. This coupling is facilitated through the open-source MED and MEDCoupling libraries of the SALOME platform. The code coupling is implemented with the MED libraries and additional routines added in the FEMuS and OpenFOAM codes. We demonstrate the accuracy, robustness, and performance of the proposed approach with examples targeting different objectives using distributed and boundary controls in each case.

Suggested Citation

  • Samuele Baldini & Giacomo Barbi & Antonio Cervone & Federico Giangolini & Sandro Manservisi & Lucia Sirotti, 2025. "Optimal Control of Heat Equation by Coupling FVM and FEM Codes," Mathematics, MDPI, vol. 13(2), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:238-:d:1565220
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/2/238/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/2/238/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:238-:d:1565220. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.