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A Thermal Fluid–Structure Interaction Problem: Modeling, Variational and Numerical Analysis

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This article presents a variational and numerical analysis for a thermal fluid–elastic structure interaction problem related to the blood flow through a vessel. We prove the existence and the uniqueness of the weak solution to the mathematical model associated with this physical problem and we establish some estimates that give the regularity for the unknown functions. Since the variational problem introduced in order to obtain these results does not provide enough regularity in the elastic domain, we approximate it with a family of viscoelastic problems, depending on a small parameter \(\varepsilon \). The viscoelastic problems contain an additional term that corresponds to the regularity “uncovered” by the initial variational problem. This approximation is justified by an error estimate theorem, followed by a convergence result. We associate to any viscoelastic problem a numerical scheme. The additional viscoelastic term allows us to establish suitable estimates for the solution to the numerical scheme, used for obtaining stability properties. Relying on these properties, we prove the convergence of the numerical scheme to the viscoelastic problem.

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Authors and Affiliations

  1. Simion Stoilow Institute of Mathematics, Romanian Academy, 21 Calea Grivitei, 014700, Bucharest, Romania

    Alexandra Ciorogar & Ruxandra Stavre

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  1. Alexandra Ciorogar
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  2. Ruxandra Stavre
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the two authors contributed equally to this work.

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Correspondence to Ruxandra Stavre.

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Communicated by K. Pileckas.

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Ciorogar, A., Stavre, R. A Thermal Fluid–Structure Interaction Problem: Modeling, Variational and Numerical Analysis. J. Math. Fluid Mech. 25, 37 (2023). https://doi.org/10.1007/s00021-023-00783-x

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