Efficient approximation of flow problems with multiple scales in time

• Verfasst von: Frei, Stefan [VerfasserIn]
• Verfasst von: Richter, Thomas [VerfasserIn]
• Titel: Efficient approximation of flow problems with multiple scales in time
• Verf.angabe: S. Frei and T. Richter
• E-Jahr: 2020
• Jahr: January 1, 2020
• Umfang: 28 S.
• Fussnoten: Gesehen am 04.08.2020
• Titel Quelle: Enthalten in: Multiscale modeling & simulation
• Ort Quelle: Philadelphia, Pa. : SIAM, 2003
• Jahr Quelle: 2020
• Band/Heft Quelle: 18(2020), 2, Seite 942-969
• ISSN Quelle: 1540-3467
• DOI: doi:10.1137/19M1258396
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1726143325

Abstract

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.