A time-adaptive algorithm for pressure dominated flows: a heuristic estimator
<|reference_start|>A time-adaptive algorithm for pressure dominated flows: a heuristic estimator: This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive algorithms based on the interplay of implicit and explicit time schemes fail to capture the fast transient dynamics of pressure fields. We present an algorithm that relies on a temporal error estimator using Backward Differentiation Formulae (BDF$k$) of order $k=2,3$. Specifically, we demonstrate that the implicit BDF$3$ solution can be well approximated by applying a single Newton-type nonlinear solver correction to the implicit BDF$2$ solution. The difference between these solutions determines our adaptive temporal error estimator. The effectiveness of our approach is confirmed by numerical experiments conducted on a backward-facing step flow CFD test case with Reynolds number $300$ and on a two-dimensional haemodynamics FSI benchmark.<|reference_end|>
@article{prusak2024a,
    title={A time-adaptive algorithm for pressure dominated flows: a heuristic
  estimator},
    author={Ivan Prusak, Davide Torlo, Monica Nonino, Gianluigi Rozza},
    journal={arXiv preprint arXiv:2407.00428},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00428},
    primaryClass={math.NA cs.NA}
}