Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics

Authors:
V. Doyeux;Y. Guyot;V. Chabannes;C. Prud'Homme;M. Ismail
Affiliations:
Université Grenoble 1/CNRS, Laboratoire Interdisciplinaire de Physique/UMR 5588 Grenoble, F-38041, France;Université Grenoble 1/CNRS, Laboratoire Interdisciplinaire de Physique/UMR 5588 Grenoble, F-38041, France;Université Grenoble 1/CNRS, Laboratoire Jean Kuntzman/UMR 5224. Grenoble, F-38041, France;Université Grenoble 1/CNRS, Laboratoire Jean Kuntzman/UMR 5224. Grenoble, F-38041, France and Université de Strasbourg/CNRS, IRMA/UMR 7501. Strasbourg, F-67000, France;Université Grenoble 1/CNRS, Laboratoire Interdisciplinaire de Physique/UMR 5588 Grenoble, F-38041, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

A new framework for two-fluid flows using a finite element/level set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells' mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as ''tank treading'' and tumbling motions.