Efficient Approximation of Flow Problems With Multiple Scales in Time

Frei, Stefan; Richter, Thomas

Efficient Approximation of Flow Problems With Multiple Scales in Time

Dateien

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Datum

2020

Autor:innen

Frei, Stefan

Richter, Thomas

DOI (zitierfähiger Link)

10.1137/19M1258396

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Multiscale Modeling & Simulation ; 18 (2020), 2. - S. 942-969. - Society for Industrial and Applied Mathematics (SIAM). - ISSN 1540-3459. - eISSN 1540-3467

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.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

FREI, 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). 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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