High Order Time Integration For Fluid-Structure Interaction on Moving Meshes

In this paper high order time integration schemes are investigated for the integration of fluid-structure interaction (FSI) model problem with deforming domains. The integration algorithm consists of a partitioned scheme in which a combination of implicit and explicit (IMEX) high order Runge-Kutta time integration schemes is used: the fluid and structure systems are decoupled at their interface and both systems are integrated using the implicit system under a given boundary condition at the interface. The influence of this boundary condition (the coupling term) is integrated using the explicit Runge-Kutta scheme. The fluid dynamics are written in the arbitrary Lagrange Eulerian formulation to cope with the deforming fluid mesh. An expression is proposed for the mesh face velocities of the deforming mesh such that the discrete geometric conservation law is satisfied. For the model problem numerical investigations are made into the efficiency of these high order time integration schemes compared to lower order methods. The IMEX scheme retains the order of the implicit and explicit schemes and obtains the same accuracy as a second order staggered scheme for less computational work.