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

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.

An energy stable one-field monolithic arbitrary Lagrangian–Eulerian formulation for fluid–structure interaction

“…In this sense, the formulation is similar to the one introduced in [4]. However it differs from [4] in the following perspectives: (1) we formulate the solid in the reference domain and analyse in an ALE frame of reference, in which case the formulation and analysis are exactly the same for two and three dimensional cases, whereas [4] formulates and analyses everything in the current domain, for which the three dimensional case is significantly more complicated [14]; (2) we update the solid deformation tensor (the F-scheme) while [4] updates the solid displacement (the d-scheme);…”

“…with F = ∂F (x, t) ∂x (14) being the deformation tensor of the solid, J Ft being the determinant of F, and Ψ (F) being the energy function of the hyperelastic solid material. Combining with the continuity equation…”

Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

“…Some methods are based on partitioned procedures, the fluid and structure sub-problems are solved separately using iterative process: fixed point iterations [1][2][3], Newton-like methods [4][5][6] or optimization techniques [7][8][9]. Monolithic methods solve the fluid-structure interaction problem as a single system of equations, [10][11][12][13], or more recently [14][15][16][17].…”

“…In [14][15][16][17], a global mesh obtained from the deformed structure mesh and a fluid mesh generated at each time step, compatible at the interface with the structure mesh are used. Remeshing the fluid domain improves the quality of the mesh in the case of large deformation.…”

Wave (Current)-Induced Pore Pressure in Offshore Deposits: A Coupled Finite Element Model

“…Considerable investigations into the wave-seabed interaction have been carried out in past decades. The methods for investigating the wave-seabed interaction problem mainly include three types, namely the uncoupled method, the semi-coupled method, and the fully coupled method [4][5][6]. The uncoupled method in investigating a wave-induced seabed response mainly occurred in earlier studies.…”