THE NUMERICAL SIMULATION OF LARGE-SCALE FLUID-STRUCTURE INTERACTION PROBLEMS IN A FULLY COUPLED FORM

Abstract. A fully coupled numerical algorithm has been developed for the numerical simu-lation 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 present arrangement of the prim-itive variables leads to a stable numerical scheme and it does not require any ad-hoc mod-ifications in order to enhance the pressure-velocity coupling. A special attention is given to satisfy the discrete continuity equation within each element at discrete level as well as the Ge-ometric Conservation Law (GCL). The nonlinear elasticity equations are discretized within the structure domain using the Galerkin finite element method. The resulting algebraic linear equations are solved in a fully coupled form. The implementation of the fully coupled pre-conditioned iterative solvers is based on the PETSc library for improving th! e efficiency of the parallel code. The present numerical algorithm is initially validated for a Newtonian fluid interacting with an elastic rectangular bar behind a circular cylinder and a three-dimensional elastic solid confined in a rectangular channel. ical Galerkin finite element is used to discretize the governing equations in a La-grangian frame. The time integration method for the structure domain is based on the New-mark type generalized− method while the first-order backward difference is used in the fluid domain. The implementation of the preconditioned coupled iterative solvers is based on the PETSc library for improving the efficiency of the parallel code. The present numerical algorithm is validated for a steady and unsteady Newtonian fluid interacting with an elastic rectangular bar behind a circular cylinder and a three-dimensional elastic solid confined in a rectangular channel