Keywords: fluid-structure interaction, partitioned strategy, weak/strong coupling.

In this paper we will explore a partitioned strategy to solve strongly coupled fluid-structure interaction problems under a moving free surface. Indeed, we will present a simulation were local fluid effects near the structure are to be modelled. The partitioned approach arise naturally when one want to model such a kind of multi-physics and multi-scale problem. It permits the use of methods and software developed independently for each of the sub-problems:

• A fluid at a large scale for the propagation of a tsunami wave, which is a fully non-linear problem for the free-surface. This problem is discretized using a boundary element method (BEM) with high order elements and solved using a Fortran code with C routines for a fast multipole algorithm [3].
• A fluid at fine scale, near the structure (for instance a coastal engineering protection), where we assume that the viscosity effect cannot be neglected. This incompressible viscous flow is discretized with a finite volume method (FVM) using a partitioned strategy to enforce the null-divergence condition. The code used is OpenFoam, a very general C++ library for the solution of fluid problems [4].
• The mechanical behavior of the structures: very complex non-linear laws that represent at the macro-scale the behavior of engineering materials can now be implemented using finite element method (FEM) based codes. This mechanical part is solved by FEAP, a FEM code programmed in Fortran [5].

As the reader can see, the different parts of our problem are really solved by different software from different research teams, and one of the goals of our work is to enforce the possibility of the re-use of existing codes in this kind of multi-physics context. Furthermore, each problem has naturally is own time scale: for instance large time steps can be used for the BEM code when computing the fluid at large scale, but the Courant condition only allows the use of small time steps in the VFM code representing the fluid at a fine scale.

Our coupling strategy is based on the Communication Template Library (CTL), a coupling middleware from the Institute of Scientific Computing [1]. The stability and the efficiency of this strategy is first verified for a benchmark fluid-structure problem with FVM and FEM components [6].

1

H.G. Matthies, R. Niekamp, J. Steindorf, "Algorithms for strong coupling procedures", Computer Methods in Applied Mechanics and Engineering, 195:2028-2049, 2006. doi:10.1016/j.cma.2004.11.032

2

M. Arnold, M. Gunther, "Preconditioned dynamic iteration for coupled differential-algebraic systems", BIT Numer. Math., 41:1-25, 2001. doi:10.1023/A:1021909032551

3

C. Fochesato, S. Grilli, F. Dias. "Numerical modeling of extreme rogue waves generated by directional energy focusing", Wave Motion, 44:395-416, 2007. doi:10.1016/j.wavemoti.2007.01.003

4

H.G. Weller, G. Tabora, H. Jasak, C. Fureby, "A tensorial approach to computational continuum mechanics using object-oriented techniques", Computers in physics, 12(6):620-631, 1998. doi:10.1063/1.168744

5

O.C. Zienkiewicz, R.L. Taylor. "The Finite Element Method". Butterworth-Heinemann, Oxford, 5th edition, 2000.

6

W.A. Wall. "Fluid-Struktur Interaktion mit stabilisierten Finiten Elementen", Phd Thesis, Institut für Baustatik, Universität Stuttgart, 1999.

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