A matrix free, partitioned solution of fluid-structure interaction problems using finite volume and finite element methods

A fully-coupled partitioned finite volume-finite volume and hybrid finite volume-finite element fluid-structure interaction scheme is presented. The fluid domain is modelled as a viscous incompressible isothermal region governed by the Navier-Stokes equations and discretised using an edge-based hybrid-unstructured vertex-centred finite volume methodology. The structure, consisting of a homogeneous isotropic elastic solid undergoing large, non-linear deformations, is discretised using either an elemental/nodal-strain finite volume approach or isoparametric Q8 finite elements and is solved using a matrix-free dual-timestepping approach. Coupling is on the solver sub-iteration level leading to a tighter coupling than if the subdomains are converged separately. The solver is parallelised for distributed-memory systems using METIS for domain-decomposition and MPI for inter-domain communication. The developed technology is evaluated by application to benchmark problems for strongly-coupled fluid-structure interaction systems. It is demonstrated that the scheme results in full coupling between the fluid and solid domains, whilst furnishing accurate solutions.