Article

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

Electronic Journal of Differential Equations 01/2009;
Source: DOAJ

ABSTRACT 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.

0 Bookmarks
 · 
91 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The present paper deals with a variant of a non conforming domain decomposition technique: the mortar finite element method. In the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices (and the edges in 3D) of subdomains. It is shown that, written under primal hybrid formulation, the approximation problem, issued from a discretization of a second order elliptic equation in 2D, is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms. Finally the parallelization advantages consequence of this variant are also addressed.
    Numerische Mathematik 11/1999; 84(2):173-197. · 1.33 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Non-conformity in the hp version can involve incompatibility in both the degrees and the meshes between adjoining subdomains. In this paper, we show how the mortar finite element method M0 and two new variants M1, M2 can be used to join together such incompatible hp sub-discretizations. Our results show optimality of the resulting non-conforming method for various h,p and hp discretizations, including the case of exponential hp convergence over geometric meshes. We also present numerical results for the Lagrange multiplier when the method is implemented via a mixed method. Three-dimensional considerations suggest that our methods M1, M2 are easier to generalize to arbitrary meshes than M0.
    Computer Methods in Applied Mechanics and Engineering 01/2000; · 2.62 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A multilevel approach with parallel implementation is developed for obtaining fast solutions of the Navier–Stokes equations solved on domains with non-matching grids. The method relies on computing solutions over different subdomains with different multigrid levels by using multiple processors. A local Vanka-type relaxation operator for the multigrid solution of the Navier–Stokes system allows solutions to be computed at the element level. The natural implementation on a multiprocessor architecture results in a straightforward and flexible algorithm. Numerical computations are presented, using benchmark applications, in order to support the method. Parallelization is discussed to achieve proper accuracy, load balancing and computational efficiency between different processors.
    Computer Methods in Applied Mechanics and Engineering 01/2006; · 2.62 Impact Factor

Full-text (2 Sources)

View
23 Downloads
Available from
May 27, 2014