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Finite Element Methods for the Temperature in Composite Media with Contact Resistance

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Abstract

We consider a heat diffusion problem inside a composite medium. The contact resistance at the interface of constitutive materials allows for jumps of the temperature field. The transmission conditions need to be handled carefully and efficiently. The main concerns are accuracy and feasibility. Hybrid dual formulations are recommended here as the most popular mixed finite elements well adapted to account for the discontinuity of the temperature field. We therefore write the discretization of the heat problem by mixed finite elements and perform its numerical analysis. Of course, applying Lagrangian finite elements is possible in simple composite media but it turns out to be problematic for complex geometries. Nevertheless, we study the convergence of this finite element method to highlight some particularities related to the model under consideration and point out the effect of the contact resistance on the accuracy. Illustrative numerical experiments are finally provided to assess the theoretical findings.

Résumé

Nous considérons une équation qui modélise la diffusion de la température dans une mousse de graphite contenant des capsules de sel. Les conditions de transition de la température entre le graphite et le sel doivent être traitées correctement. Nous effectuons l’analyse de ce modèle et prouvons qu’il est bien posé. Puis nous en proposons une discrétisation par éléments finis et effectuons l’analyse a priori du problème discret. Quelques expériences numériques confirment l’intérêt de cette approche.

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Acknowledgments

We are deeply grateful to Professor Vivette Girault for valuable discussion on the subject of the paper.

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Authors and Affiliations

  1. UTC, EA 2222, LMAC, Sorbonne Universités, 60205, Compiègne, France

    Faker Ben Belgacem

  2. CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France

    Christine Bernardi

  3. UPMC Univ Paris 06, UMR 7598, LJLI, Sorbonne Universités, 75005, Paris, France

    Christine Bernardi

  4. UB1-I2M UMR CNRS 5295, Université de Bordeaux, 33405, Talence, France

    Faten Jelassi & Maimouna Mint Brahim

  5. ENIT-LAMSIN, BP 37, 1002, Tunis, Tunisia

    Faten Jelassi

Authors
  1. Faker Ben Belgacem
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  2. Christine Bernardi
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  3. Faten Jelassi
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  4. Maimouna Mint Brahim
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Correspondence to Christine Bernardi.

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Ben Belgacem, F., Bernardi, C., Jelassi, F. et al. Finite Element Methods for the Temperature in Composite Media with Contact Resistance. J Sci Comput 63, 478–501 (2015). https://doi.org/10.1007/s10915-014-9907-0

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  • DOI: https://doi.org/10.1007/s10915-014-9907-0

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