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Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation

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Fluid-Structure Interaction and Biomedical Applications

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

Fluid–structure interaction (FSI) problems arise in many applications. They include multi-physics problems in engineering such as aeroelasticity and propeller turbines, as well as biofluidic application such as self-propulsion organisms, fluid–cell interactions, and the interaction between blood flow and cardiovascular tissue. A comprehensive study of these problems remains to be a challenge due to their strong nonlinearity and multi-physics nature. To make things worse, in many biological applications the structure is composed of several layers, each with different mechanical characteristics. This is, for example, the case with arterial walls, which are composed of three main layers: the intima, media, and adventitia, separated by thin elastic laminae. A stable and efficient FSI solver that simulates the interaction between an incompressible, viscous fluid and a multi-layered structure would be an indispensable tool for the computational studies of solutions.

The multi-physics nature of this class of problems suggests the use of partitioned, modular algorithms based on an operator splitting approach that would separate the different physics in the problem. This chapter presents such a scheme, which can be used not only in computations, but also to prove existence of weak solutions to this class of problems. Particular attention will be payed to multi-physics FSI problems involving structures consisting of multiple layers.

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Acknowledgements

The research of the authors has been supported in part by the National Science Foundation under the following grants: NIGMS DMS-1263572, DMS-1318763, DMS-1311709, DMS-1262385, DMS-1109189, and by the Texas Higher Education Board under grant ARP-003652-0023-2009.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, USA

    Sunčica Čanić

  2. Faculty of Science, Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Boris Muha

  3. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA

    Martina Bukač

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  1. Sunčica Čanić
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  2. Boris Muha
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Correspondence to Sunčica Čanić .

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  1. Department of Technical Mathematics, Czech Technical University in Prague, Prague, Czech Republic

    Tomáš Bodnár

  2. Swanson School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

    Giovanni P. Galdi

  3. Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague 1, Czech Republic

    Šárka Nečasová

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Čanić, S., Muha, B., Bukač, M. (2014). Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation. In: Bodnár, T., Galdi, G., Nečasová, Š. (eds) Fluid-Structure Interaction and Biomedical Applications. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0822-4_2

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