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

Chen-Yu Chiang 1, 2 Olivier Pironneau 2 Tony Sheu 1 Marc Thiriet 3
3 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, UPMC - Université Pierre et Marie Curie - Paris 6, Inria de Paris
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.
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Chen-Yu Chiang, Olivier Pironneau, Tony Sheu, Marc Thiriet. Numerical Study of a 3D Eulerian Monolithic Formulation for Incompressible Fluid-Structures Systems. Fluids, MDPI, 2017, Mechanics of Fluid-Particles Systems and Fluid-Solid Interactions, 2 (2), pp.34-53. ⟨10.3390/fluids2020034⟩. ⟨hal-01558747⟩

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