A computational domain decomposition approach for solving coupled flow-structure-thermal interaction problems

Electronic Journal of Differential Equations (Impact Factor: 0.52). 01/2009;
Source: DOAJ


Solving complex coupled processes involving fluid-structure-thermal interactions is a challenging problem in computational sciences and engineering. Currently there exist numerous public-domain and commercial codes available in the area of Computational Fluid Dynamics (CFD), Computational Structural Dynamics (CSD) and Computational Thermodynamics (CTD). Different groups specializing in modelling individual process such as CSD, CFD, CTD often come together to solve a complex coupled application. Direct numerical simulation of the non-linear equations for even the most simplified fluid-structure-thermal interaction (FSTI) model depends on the convergence of iterative solvers which in turn rely heavily on the properties of the coupled system. The purpose of this paper is to introduce a flexible multilevel algorithm with finite elements that can be used to study a coupled FSTI. The method relies on decomposing the complex global domain, into several local sub-domains, solving smaller problems over these sub-domains and then gluing back the local solution in an efficient and accurate fashion to yield the global solution. Our numerical results suggest that the proposed solution methodology is robust and reliable.

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    ABSTRACT: This paper deals with multilevel domain decomposition techniques inside a multigrid framework to solve fluidstructure interaction (FSI) problems via the Finite Element Method (FEM). The mathematical problem consists of the Navier-Stokes equations in the Arbitrary-Lagrangian-Eulerian (ALE) formulation coupled with a non-linear incompressible structure model (Neo-Hookean). The coupling between the structure and the fluid, due to the important added-mass effect, is enforced within a unique solver. This kind of problem can be tackled efficiently by domain decomposition techniques. The solution strategy presented in this work is to solve several small local subproblems over subdomain patches using Vanka smoothing inside a multigrid algorithm. The results of a benchmark are presented in order to show the potentiality of the proposed solution method in terms of accuracy and efficiency.
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