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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 15
INNOVATION IN ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero, R. Montenegro
Chapter 13
SubStructuring Method for FluidStructure Interaction Problems with NonMatching Grids F. Magoulès* and F.X. Roux+
*Applied Mathematics and Systems Laboratory (MAS), Ecole Centrale Paris, ChâtenayMalabry, France F. Magoulès, F.X. Roux, "SubStructuring Method for FluidStructure Interaction Problems with NonMatching Grids", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Innovation in Engineering Computational Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 13, pp 269285, 2006. doi:10.4203/csets.15.13
Keywords: fluidstructure interaction, coupled problem, nonconforming meshes, iterative method, substructuring, parallel computing.
Summary
Many areas of engineering and physics require powerful algorithms to
solve huge problems. Substructuring methods and preconditioning
techniques based on domain
decomposition [1,4,5,7]
are very efficient for computing the solution of large
scale problems in parallel. These methods mainly consist of splitting the global
domain into several subdomains and computing the solution on the
global domain through the solution of the problems associated with
each subdomain. Major research has been done on these techniques and methods during the
last fifteen years. Novel algorithms, new preconditioners and new fields of application have been
successfully investigated. One of the current research challenges in
the field when handling reallife engineering problems consists of
solving coupled problems.
In this paper a general methodology to solve coupled fluidstructure problems is presented. The proposed coupling is usually called 'weakcoupling' in the literature because the equations are coupled through the boundary conditions and the coupling occurs on the right hand side only. The proposed method is based on a substructuring method, where each subdomain consists of a singlephysics problem. Coupling between the subdomains is insured through coupled quantities. A locally optimal preconditioning technique based on the exact solution of fluid and structure, independent subproblems, is proposed here. A key property of the iterative solution of the preconditioned coupled problem is that only the restrictions on the interface of the vectors built at each iteration need to be stored, making the implementation of the robust Krylov method, with full orthogonalization, inexpensive. In addition, at each iteration, each independent (singlephysics) subproblem is solved in parallel. When dealing with coupled fluidstructure interaction problems, one major difficulty lies in the nonmatching grids between the mesh of the fluid and the mesh of the structure. In Figure 1 is an example of nonmatching grids between the structural mesh of a car body, and the associated acoustic mesh of a car compartment, which clearly outlines this difficulty. Contrary to the MpCCI [3] software based on a mortar finite element discretization on the fluidstructure interface, this paper proposes to integrate the coupled quantities on a set of quadrature points. This approach only involves the computation of nodal values and interpolation at given Gauss points, which allows any refinement.In the numerical experiments the evaluation of the frequency response function of a driver's ear, due to vibration of a car body, is investigated. This example is representative of a wider class of problems where one tries to evaluate the acoustic response within a cavity as induced by some vibrations. The singlephysics problems are solved respectively with MSC [2] for the vibroelasticity analysis and with SYSNOISE [6] for the acoustic analysis. An additional coupling module is used to manage coupling between the singlephysics problems. References
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