A multilevel domain decomposition approach to solving coupled applications in computational fluid dynamics

Direct numerical simulation of the non-linear equations, governing a fluid-structure system, relies heavily on the properties of the coupled system and the corresponding iterative solver. The purpose of this paper is to introduce a flexible and robust multilevel finite element algorithm that can be used to study the behavior of a fully coupled fluid-structure system. The method relies on the domain decomposition characteristics of the multigrid Vanka solvers, which decompose the complex global domain into the finite element local sub-domains and then compute the global solution iteratively. This particular methodology allows us to solve easily this coupled system over a fluid-solid domain which consists of a set of subdomains from different mesh levels with conforming or non-conforming finite element method approximations. The multigrid projection and restriction operators are used to impose the matching between the extended fluid and solid velocity field.