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Fluids 2017, 2(2), 34; doi:10.3390/fluids2020034

Numerical Study of a 3D Eulerian Monolithic Formulation for Incompressible Fluid-Structures Systems

1
Department of Engineering Science and Ocean Engineering, National Taiwan University; Taipei 10617, Taiwan
2
Laboratoire Jacques-Louis-Lions (LJLL), Sorbonne University, UPMC (Paris VI), 75005 Paris, France
3
Institute of Applied Mathematical Sciences and Center of Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taipei 10617, Taiwan
4
INRIA-Paris-Rocquencourt, EPC-REO project, Domaine de Voluceau, BP105, 78153 Le Chesnay Cedex, France
Current address: LJLL-UPMC, boite 187, 4 Place Jussieu, F75005 Paris, France.
*
Author to whom correspondence should be addressed.
Received: 27 March 2017 / Revised: 31 May 2017 / Accepted: 8 June 2017 / Published: 16 June 2017
(This article belongs to the Special Issue Mechanics of Fluid-Particles Systems and Fluid-Solid Interactions)
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Abstract

An algorithm is derived for a hyperelastic incompressible solid coupled with a Newtonian fluid. It is based on a Eulerian formulation of the full system in which the main variables are the velocities. After a fully implicit discretization in time it is possible to eliminate the displacements and solve a variational equation for the velocities and pressures only. The stability of the method depends heavily on the use of characteristic-Galerkin discretization of the total derivatives. For comparison with previous works, the method is tested on a three-dimensional (3D) clamped beam in a pipe filled with a fluid. Convergence is studied numerically on an axisymmetric case. View Full-Text
Keywords: fluid-structure-interaction; Eulerian formulation; monolithic; finite element; characteristic-Galerkin; large displacement; energy compatible algorithm fluid-structure-interaction; Eulerian formulation; monolithic; finite element; characteristic-Galerkin; large displacement; energy compatible algorithm
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chiang, C.-Y.; Pironneau, O.; Sheu, T.W.H.; Thiriet, M. Numerical Study of a 3D Eulerian Monolithic Formulation for Incompressible Fluid-Structures Systems. Fluids 2017, 2, 34.

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