A Monolithic Fem Solver for an Ale Formulation of Fluid–structure Interaction with Configuration for Numerical Benchmarking

Abstract. We investigate a monolithic algorithm to solve the problem of time dependent interaction between an incompressible viscous fluid and an elastic solid. The continuous formulation of the problem and its discretization is done in a monolithic way, treating the problem as one continuum. The Q2/P dis 1 finite elements are used for the discretization and an approximate Newton method with coupled multigrid linear solver is developed for solving the equations. We discuss possible efficient strategies of setting up the resulting system and its solution. A 2-dimensional configuration is presented to test the developed method. It is based on the older successful DFG benchmark flow around cylinder for incompressible laminar fluid flow. Similar to this older benchmark we consider the flow to be incompressible and in the laminar regime. The structure is allowed to be compressible or incompressible and the deformations of the structure are periodic and significant in terms of displacement. This configuration can be used to compare different numerical methods and code implementations for the fluid-structure interaction problem qualitatively and particularly quantitatively with respect to efficiency and accuracy of the computation.