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Added Mass Partitioned Fluid–Structure Interaction Solver Based on a Robin Boundary Condition for Pressure

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Abstract

This paper describes a self-contained, partitioned fluid–structure interaction solver based on a finite volume discretisation. The incompressible fluid flow is described by the Navier–Stokes equations in the arbitrary Lagrangian–Eulerian form and the solid deformation is described by the St. Venant-Kirchhoff hyperelastic model in the total Lagrangian form. Both fluid and solid are discretised in space using the second-order accurate cell-centred finite volume method, and temporal discretisation is performed using the first-order accurate implicit Euler scheme. Coupling between fluid and solid is performed using a Robin-Neumann partitioned procedure based on a new Robin boundary condition for pressure. The solver has been tested on the wave propagation in an elastic tube test case characterised by a low solid-to-fluid density ratio. The first-order temporal accuracy is shown and the stability of the method is demonstrated for both the strongly coupled and loosely coupled versions of the solution procedure. It is also shown that the proposed methodology can efficiently handle FSI cases in which the fluid domain is entirely enclosed by Dirichlet boundary conditions, even for the case of geometrically nonlinear elastic deformation.

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Notes

  1. 1.

    It is assumed that for the considered test case (large artery and small pressure change), the blood can be considered as an incompressible Newtonian fluid.

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Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

    Željko Tuković & Hrvoje Jasak

  2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, South Bend, IN, USA

    Martina Bukač

  3. School of Mechanical and Materials Engineering, University College Dubin, Bekaert University Technology Centre, Dublin, Ireland

    Philip Cardiff & Alojz Ivanković

Authors
  1. Željko Tuković
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  2. Martina Bukač
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  3. Philip Cardiff
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  4. Hrvoje Jasak
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  5. Alojz Ivanković
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Correspondence to Željko Tuković .

Editor information

Editors and Affiliations

  1. Department of Polymer Engineering, University of Minho, Guimarães, Portugal

    J. Miguel Nóbrega

  2. University of Zagreb, Zagreb, Croatia

    Hrvoje Jasak

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Tuković, Ž., Bukač, M., Cardiff, P., Jasak, H., Ivanković, A. (2019). Added Mass Partitioned Fluid–Structure Interaction Solver Based on a Robin Boundary Condition for Pressure. In: Nóbrega, J., Jasak, H. (eds) OpenFOAM® . Springer, Cham. https://doi.org/10.1007/978-3-319-60846-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-60846-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60845-7

  • Online ISBN: 978-3-319-60846-4

  • eBook Packages: EngineeringEngineering (R0)

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