Efficient Approximation of Flow Problems With Multiple Scales in Time

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2020
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Richter, Thomas
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Multiscale Modeling & Simulation. Society for Industrial and Applied Mathematics (SIAM). 2020, 18(2), pp. 942-969. ISSN 1540-3459. eISSN 1540-3467. Available under: doi: 10.1137/19M1258396
Zusammenfassung

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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510 Mathematik
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ISO 690FREI, Stefan, Thomas RICHTER, 2020. Efficient Approximation of Flow Problems With Multiple Scales in Time. In: Multiscale Modeling & Simulation. Society for Industrial and Applied Mathematics (SIAM). 2020, 18(2), pp. 942-969. ISSN 1540-3459. eISSN 1540-3467. Available under: doi: 10.1137/19M1258396
BibTex
@article{Frei2020-05-26Effic-50387,
  year={2020},
  doi={10.1137/19M1258396},
  title={Efficient Approximation of Flow Problems With Multiple Scales in Time},
  number={2},
  volume={18},
  issn={1540-3459},
  journal={Multiscale Modeling & Simulation},
  pages={942--969},
  author={Frei, Stefan and Richter, Thomas}
}
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