  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.
