A parallel fully coupled approach for large-scale fluid-structure interaction problems

A fully coupled numerical algorithm has been developed for the numerical simulation of large-scale fluid structure interaction problems. The incompressible Navier-Stokes equations are discretized using an Arbitrary Lagrangian-Eulerian (ALE) formulation based on the side-centered unstructured finite volume method. The side-centered arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance the pressure-velocity coupling. The continuity equation is satisfied within each element exactly and the summation of the continuity equations can be exactly reduced to the domain boundary, which is important for the global mass conservation. A special attention is also given to satisfy the discrete geometric conservation law (DGCL). The nonlinear elasticity equations are discretized within the structure domain using the Galerkin finite element method. The structural behaviour of solid domain is governed by the the constitutive laws for the nonlinear Saint Venant-Kirchhoff material. The resulting algebraic nonlinear equations are solved in a fully coupled form using the restricted additive Schwarz method with the flexible GMRES(m) algorithm. The implementation of the fully coupled preconditioned iterative solvers is based on the PETSc library for improving the efficiency of the parallel code. The present numerical algorithm is validated for a Newtonian fluid interacting with an elastic rectangular bar behind a circular cylinder, a three-dimensional elastic solid confined in a rectangular channel and a pulsatile flow in a flexible tube, which mimics the case of pulsatile blood flow through elastic arteries.