Fast Solvers for Unsteady Thermal Fluid Structure Interaction
  We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a refence solver a previously developed efficient time adaptive higher order time integration scheme is used.   To improve upon this, we work on reducing the number of fixed point coupling iterations. Thus, first widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested. In particular, Aitken relaxation, minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are considered. Second, we explore the idea of extrapolation based on data given from the time integration and derive such methods for SDIRK2. While the vector extrapolation methods have no beneficial effects, the extrapolation methods allow to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic. 
Philipp Birken, Tobias Gleim, Detlef Kuhl and Andreas Meister
math.NA