Approximation of time-periodic flow past a translating body by flows in bounded domains
Authors
- Eiter, Thomas
ORCID: 0000-0002-7807-1349 - Silvestre, Ana Leonor
ORCID: 0000-0001-5972-3033
2020 Mathematics Subject Classification
- 35Q30 76D05 76D07 35B10
Keywords
- Time-periodic solutions, incompressible Navier--Stokes flows, exterior domains, Oseen flows, fundamental solution, artificial boundary conditions, approximation, truncation error
DOI
Abstract
We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow within truncated domains, incorporating appropriate artificial boundary conditions. For these bounded domain problems, we prove the existence and uniqueness of weak solutions. Finally, we estimate the error in the velocity component as a function of the truncation radius, showing that, as the latter passes to infinity, the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow.
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