Keywords: fluid-structure interactions, CFD, cantilevered beam.

This paper will describe the development of a modular fluid-structure interaction (FSI) code as well as present results for a few test cases that were used to validate the code. The code that is being developed will be used to simulate several problems of interest, from aeroelasticity problems to sub-sea propulsion using shape deformation. In short, the present work has, as an objective, the creation of a FSI code which is general in nature and that can be applied to a host of different cases.

Two different approaches can be taken when creating a FSI code. The first is to create a 'monolithic' code which couples both the fluid and structural dynamics implicitly and solves the two fields simultaneously. While this is advantageous in that the fields are implicitly coupled, it has the drawback that the coding has to be done for both problems, which can be a lengthy process. By utilizing a modular approach, existing independent computational fluid and solid dynamics (CFD and CSD respectively) codes can be used. This allows for the use of excellent existing codes, which yields higher quality results.

The modular approach has been used by several researchers with great success such as Raveh [5], Pirzadeh [4], Bendiksen [1] and Farhat et al [2,3].

Broadly speaking, the cycle consists of six steps or modules:

1. In the pre-processing module, the fluid and structural grids are created and the problem is initialized.
2. The mesh is received and the forces on the structure are calculated.
3. The CSD solver moves one step in time and updates the structure.
4. The deformations obtained from the CSD solver are mapped onto the fluid grid.
5. The fluid grid is deformed to accommodate the new structure.
6. The new fluid grid is used to move the fluid solver one step in time and the flow field is updated.

Steps 2 through 6 are repeated until the simulation is completed.

The CFD code used is a block structured finite volume code called SPARC (Structured PArallel Research Code) developed at the University of Karlsruhe in Germany. This codes offers several turbulence models along with a dual time step algorithm which circumvents the time step limit imposed by explicit codes. It has the additional advantage of being a parallel architecture code, which allows for the simulation of complex flows.

The CSD module is an in-house code developed at the University of Victoria. It uses Mindlin-Reissner plate elements to simulate the structural deformation. For now, the code is linear and is therefore limited to small deformations. This will be altered in the future.

The mesh deformation module was also developed in house and uses the arc-length method to deform the mesh. This method is well suited to multi-block topologies and large deformations.

Several test cases will be presented, including a 2D static and oscillating cylinder which will serve to validate the CFD code used. The CSD solver is also tested using a well known benchmark: the simply supported flat plate with uniform load. Finally, the full FSI code is tested using a cantilevered plate in uniform flow.

1

O. Bendiksen. "Fluid-structure coupling requirements for time-accurate aeroelastic simulations." In "4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise, volume 3, pages 89-104. ASME, Dallas, Texas, USA, 1997.

2

C. Farhat, M. Lesoinne, P. LeTallec. "Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Computer Methods in Applied Mechanics and Engineering, 157, 95-114, 1998. doi:10.1016/S0045-7825(97)00216-8

3

C. Farhat, K. Pierson, C. Degand. "Multidisciplinary simulation of the maneuvering of an aircraft. Engineering with Computers, 17, 16-27, 2001. doi:10.1007/PL00007193

4

S. Z. Pirzadeh. "An adaptive unstructured grid method dy grid subdivision, local remeshing, and grid movement. In "14th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, Norfolk, Virginia, 1999.

5

D. E. Raveh. "Reduced order models for nonlinear unsteady aerodynamics. In "8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, American Institute of Aeronautics and Astronautics, Long Beach, CA, 2000.

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