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Fluids-membrane interaction with a full Eulerian approach based on the level set method

Dalmon, Alexis and Kentheswaran, Kalyani and Mialhe, Guillaume and Lalanne, Benjamin and Tanguy, Sébastien Fluids-membrane interaction with a full Eulerian approach based on the level set method. (2020) Journal of Computational Physics, 406. ISSN 0021-9991

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Official URL: https://doi.org/10.1016/j.jcp.2019.109171

Abstract

A fully Eulerian approach to predict fluids-membrane behaviours is presented in this paper. Based on the numerical model proposed by Ii et al. (2012), we present a sharp methodology to account for the jump conditions due to hyperelastic membranes. The membrane is considered infinitely thin and is represented by the level set method. Its deformations are obtained from the transport of the components of the left Cauchy-Green tensor throughout time. Considering the linear or a hyperelastic material law, the surface stress tensor is computed and gives the force exerted by the membrane on the surrounding fluids. The membrane force is taken into account in the Navier-Stokes equations as jump conditions on the pressure and on the velocity derivatives by imposing suitable singular source terms in cells crossed by the interface. To prevent stability issues, an extension algorithm has been developed to remove the normal derivatives of the scalar fields specific to the membrane. In particular, a subcell resolution at the interface of the extrapolated variable is proposed for increasing the accuracy of the extension algorithm. These improvements are validated by comparing our numerical results with benchmarks from the literature. Moreover, a new benchmark is proposed for fluids with both different viscosities and different densities to target applications where a gas and a liquid phase are separated by a membrane.

Item Type:Article
HAL Id:hal-02518729
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National d'Études Spatiales - CNES (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Institut national de recherche pour l'agriculture, l'alimentation et l'environnement - INRAE (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:19 Oct 2021 12:19

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