Space-time fluid-structure interaction with space-time error control and adaptivity in discretization errors and reduced order modeling

In this project, first a space-time implementation of monolithic FSI shall be
derived. Here, the temporal discretization is based on a discontinuous Galerkin
(dG) method. This allows to obtain numerically stable higher order time inte-
gration schemes. The resulting model and implementation shall be tested with
the FSI-2 and FSI-3 Hron/Turek benchmarks.
In the second phase, space-time error control and adaptivity will be addressed.
Therein, a posteriori goal-oriented error estimation is based on the dual-weighted
residual method and the error localization is done with a partition-of-unity. Er-
ror reductions, estimator reductions, and effectivity indices shall be studied for
a sequence of locally refined meshes.
Finally, the error estimator shall be extended to control model order reductions
in which snapshots of the full order model are used to construct a reduced
order model. Here, the decision which snapshots are adopted shall be decided
again with goal-oriented error estimation. An interesting application of this
framework is towards optimal control in which the single models run several
times and therefore reduced order modeling helps to reduce significantly the
computational cost.

Doctoral Researcher: Ramakrishnan Chandran

Scientific Advisor: Thomas Wick, Amelie Fau.