Violent Fluid-Structure Interaction simulations using a coup

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Violent Fluid-Structure Interaction simulations using a coupled SPH/FEM method

G Fourey1, G Oger2, D Le Touzé1 and B Alessandrini1

1

2 Fluid Mechanics Lab., Ecole Centrale Nantes / CNRS, Nantes, France HydrOcean, Nantes, France

E-mail: guillaume.fourey@ec-nantes.fr

Abstract. The Smoothed Particle Hydrodynamics (SPH) method presents different key assets

for modelling violent Fluid-Structure Interactions (FSI). First, this method is a meshless

method, which drastically reduces the complexity of handling the fluid-structure interface

when using SPH to model the fluid and coupling it with a Finite Element Method (FEM) for

the solid. Second, the method is Lagrangian and large deformations of the fluid domain can

thus be followed, which is especially interesting for simulating violent interactions in presence

of a free surface, or which induce large deformations, rotations, and translations of the solid.

Third, the SPH method being explicit, the time scale of the SPH resolution in the fluid domain

is naturally adapted to the FEM resolution in the solid. Free-surface FSIs can also be simulated

without including the air phase when it does not play a significative role. For violent

interactions where the fluid compressibility matters, it is also intrinsically modelled by the SPH

method. The paper details the SPH method used and the coupling. The FEM solver is a

standard open source solver for solid mechanics. Validation test cases are then presented in

detail. They include the hydrodynamic impact of elastic wedges at high speed, where local

pressures and wedge deformations are compared to experimental data.

1. Introduction

Nowadays, thanks to the growth of computing power numerical simulation is widely used to study complex physical problems involving fluids or solids. The modeling of coupled phenomena such as fluid-structure interactions can be carried out as well even though their simulation needs important numerical resources. In literature different methods have been developed in order to predict the deformations of a structure due to non-stationary loads caused by fluid flow, itself modified by the structure evolution. The complexity of the coupling and its simulation is much increased when both the fluid and the structure are largely deformed due to their interaction. We concentrate here on these complex fluid-structure interactions.

In a general way Lagrangian formulations based on the Finite Element Method (FEM) are employed to study the structure behaviour. The mesh follows solid deformations. However, different methods which allow following the moving interface between fluid and solid are used to simulate the fluid evolution when dealing with fluid-structure interaction problems. We can cite mesh-based methods such as Lagrangian or Arbitrary Lagrangian Eulerian (ALE) formulations of Navier-Stokes equations, often using the Finite Volume Method (FVM) or FEM [1], where the fluid mesh is deformed to adapt to the solid domain deformation. This adaptation is costly and of complex implementation. Further, large fluid domain deformations cannot be handled without using remeshing

methods which significantly increase CPU costs of simulations. Another way to solve this problem is to use Volume of Fluid method (VOF) or Level-Set methods which permit to track interfaces on fixed grids [2]. With all these methods, a contact algorithm is used in order to prevent materials interpenetration. Fluid structure simulations have also been performed using the Boundary Element Method (BEM) [3]. In the latter case, only boundaries need to be meshed. However, this is limited to simplified problems in terms of geometry (of the free surface especially) and physics (no vorticity nor viscosity).

Particle-based methods have also been used to model fluid evolution in the context of Fluid-Structure Interactions. Is for instance the case with the Material Point Method in [4], or with the Particle Finite Element Method (PFEM) in [5]. However these methods are not fully meshless.

The method proposed here to simulate fluid-structure interactions relies on the Smoothed Particle Hydrodynamics method (SPH) [7][8][9] resolution of the fluid problem. The latter method being Lagrangian and meshless, no free surface tracking techniques and contact algorithm between fluid and structure domains are needed. In addition, compressibility effects are taken into account when they matter. In this paper, we first present an introduction to the SPH formalism. Then, the way we couple this method to a standard FEM solver for the solid is described. Validation is made on the hydrodynamic impact of an elastic wedge in comparison to the analytical solution. An illustrative test case is then presented where a water column impacts an elastic plate resulting on a strong interaction with a very complex flow pattern.

2. SPH solver

In 1977, the SPH method was proposed by Monaghan, Gingold and Lucy [10][11]. The aim was to simulate complex astrophysical phenomena such as star formations. Later, Monaghan used this method to simulate free surface flows [12].

2.1. Governing equations

As we focus on fast dynamics cases (regarding the fluid, the solid answer being of slow dynamics), viscosi …… 此处隐藏：5801字，全部文档内容请下载后查看。喜欢就下载吧 ……