Parallel time-stepping for fluid–structure interactions

Abstract

We present a parallel time-stepping method for fluid–structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space is based on equal order finite element for all variables and a variant of the Crank-Nicolson scheme is used as second order time integrator. To accelerate the solution of the systems, we analyze a parallel-in time method. For different numerical test cases in 2d and in 3d we present the efficiency of the resulting solution approach. We also discuss some challenges and limitations that are connected to the special structure of fluid–structure interaction problem. In particular, we will investigate stability and dissipation effects of the time integration and their influence on the convergence of the parareal method. It turns out that especially processes based on an internal dynamics (e.g.driven by the vortex street around an elastic obstacle) cause great difficulties. Configurations however, which are driven by oscillatory problem data, are well-suited for parallel time stepping and allow for substantial speedups.