B4.: 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 fluid-structure interaction shall be derived. Here, the temporal discretization is based on a discontinuous Galerkin (dG) method. This allows to obtain numerically stable higher order time integration 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. Error 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.

[1] L. Failer, T. Wick; Adaptive Time-Step Control for Nonlinear Fluid-Structure Interaction, Journal of Computational Physics (JCP), Vol. 366, 2018, pp. 448 - 477

[2] T. Wick, W. Wollner; Optimization with nonstationary, nonlinear monolithic fluid-structure interaction, International Journal for Numerical Methods in Engineering (IJNME), Vol. 122 (19), 2021, pp. 5430-5449

[3] Hendrik Fischer, Julian Roth, Thomas Wick, Ludovic Chamoin, Amelie Fau; MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM, 2023, arXiv:2304.01140

[4] Hendrik Fischer, Julian Roth, Ludovic Chamoin, Amelie Fau, Mary F. Wheeler, Thomas Wick; Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity, 2023, arXiv:2311.08907

[5] P. Junker, T. Wick; Space-time variational material modeling: a new paradigm demonstrated for thermo-mechanically coupled wave propagation, visco-elasticity, elasto-plasticity with hardening, and gradient-enhanced damage, Computational Mechanics (CM), Aug 2023, published online

Supervision: Prof. Dr. Thomas Wick (LUH), NN (ENS)