A time-adaptive algorithm for pressure dominated flows: a heuristic estimator
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913409700724736 |
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| author | Prusak, Ivan Torlo, Davide Nonino, Monica Rozza, Gianluigi |
| author_facet | Prusak, Ivan Torlo, Davide Nonino, Monica Rozza, Gianluigi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A time-adaptive algorithm for pressure dominated flows: a heuristic estimator Prusak, Ivan Torlo, Davide Nonino, Monica Rozza, Gianluigi Numerical Analysis 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. |
| title | A time-adaptive algorithm for pressure dominated flows: a heuristic estimator |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.00428 |