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

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 fem approximations. The multigrid projection and restriction operators are used to impose the matching between the extended fluid and solid velocity field.