Efficient approximation of flow problems with multiple scales in time
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier--Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on a slow scale in time. We derive an averaging scheme that i...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 1, 2020
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| In: |
Multiscale modeling & simulation
Year: 2020, Volume: 18, Issue: 2, Pages: 942-969 |
| ISSN: | 1540-3467 |
| DOI: | 10.1137/19M1258396 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/19M1258396 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/abs/10.1137/19M1258396 
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| Author Notes: | S. Frei and T. Richter |
| Summary: | In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier--Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on a slow scale in time. We derive an averaging scheme that is of first order with respect to the ratio of time scales $\epsilon$. In order to cope with the problem of unknown initial data for the fast-scale problem, we assume near-periodicity in time. Moreover, we construct a second-order accurate time discretization scheme and derive a complete error analysis for a corresponding simplified ODE system. The resulting multiscale scheme does not ask for the continuous simulation of the fast-scale variable and shows powerful speedups up to 1:10,000 compared to a resolved simulation. Finally, we present some numerical examples for the full Navier--Stokes system to illustrate the convergence and performance of the approach. |
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| Item Description: | Gesehen am 04.08.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1540-3467 |
| DOI: | 10.1137/19M1258396 |