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A Monolithic Approach to Fluid–Composite Structure Interaction

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Abstract

We study a nonlinear fluid–structure interaction (FSI) problem between an incompressible, viscous fluid and a composite elastic structure consisting of two layers: a thin layer (membrane) in direct contact with the fluid, and a thick layer (3D linearly elastic structure) sitting on top of the thin layer. The coupling between the fluid and structure, and the coupling between the two structures is achieved via the kinematic and dynamic coupling conditions modeling no-slip and balance of forces, respectively. The coupling is evaluated at the moving fluid–structure interface with mass, i.e., the thin structure. To solve this nonlinear moving-boundary problem in 3D, a monolithic, fully implicit method was developed, and combined with an arbitrary Lagrangian–Eulerian approach to deal with the motion of the fluid domain. This class of problems and its generalizations are important in e.g., modeling FSI between blood flow and arterial walls, which are known to be composed of several different layers, each with different mechanical characteristics and thickness. By using this model we show how multi-layered structure of arterial walls influences the pressure wave propagation in arterial walls, and how the presence of atheroma and the presence of a vascular device called stent, influence intramural strain distribution throughout different layers of the arterial wall. The detailed intramural strain distribution provided by this model can be used in conjunction with ultrasound B-mode scans as a predictive tool for an early detection of atherosclerosis (Zahnd et al. in IEEE international on ultrasonics symposium (IUS), pp 1770–1773, 2011).

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Acknowledgements

All the authors would like to thank Professor Alfio Quarteroni for his support of this research and of D. Forti’s visit to UH. Additionally, the research of D. Forti was supported by the Swiss National Foundation (SNF), Project No. 140184. S. Deparis and D. Forti gratefully acknowledge the Swiss National Supercomputing Center (CSCS) for providing the CPU resources for the numerical simulations under Project ID s475. The research of S. Canic and M. Bukac was supported by the US National Science Foundation under Grant DMS-1318763, which also provided partial support for D. Forti’s visit to the University of Houston. Additionally, the research of M. Bukac was supported by the US National Science Foundation under Grant DMS-1619993. The research of S. Canic and A. Quaini was supported by the US National Science Foundation under Grant DMS-1263572. Additionally, the research of A. Quaini was supported by the US National Science Foundation under Grant DMS-1620384. Additionally, the research of S. Canic was supported by NSF DMS-1311709 and by the University of Houston Hugh Roy and Lillie Cranz Cullen Distinguished Professorship funds, which also provided additional travel support for D. Forti’s visit to UH. The authors acknowledge the use of the Maxwell Cluster and the advanced support from the Center of Advanced Computing and Data Systems at the University of Houston to carry out the research presented here.

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Authors and Affiliations

  1. CMCS - Chair of Modeling and Scientific Computing, MATHICSE - Mathematics Institute of Computational Science and Engineering, EPFL - École Polytechnique Fédérale de Lausanne, Station 8, Lausanne, 1015, Switzerland

    Davide Forti & Simone Deparis

  2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, 158 Hurley Hall, Notre Dame, IN, 46556, USA

    Martina Bukac

  3. Department of Mathematics, University of Houston, 4800 Calhoun Rd, Houston, TX, 77204, USA

    Annalisa Quaini & Suncica Canic

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  1. Davide Forti
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Correspondence to Annalisa Quaini.

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Forti, D., Bukac, M., Quaini, A. et al. A Monolithic Approach to Fluid–Composite Structure Interaction. J Sci Comput 72, 396–421 (2017). https://doi.org/10.1007/s10915-017-0363-5

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