Computation of Steady Incompressible Flows in Unbounded Domains

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Authors
Gustafsson, Jonathan
Protas, Bartosz
Subjects
Steady Navier-Stokes system
unbounded domains
wake flows
spectral methods
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2015-01
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Abstract
In this study we revisit the problem of computing steady Navier- Stokes flows in two-dimensional unbounded domains. Precise quanti- tative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical fluid dynamics. Following a review of key mathematical properties of such solutions related to the slow decay of the velocity field at large distances from the obstacle, we develop and carefully validate a spectrally-accurate computational approach which ensures the correct behavior of the solution at infin- ity. In the proposed method the numerical solution is defined on the entire unbounded domain without the need to truncate this domain to a finite box with some artificial boundary conditions prescribed at its boundaries. Since our approach relies on the streamfunction- vorticity formulation, the main complication is the presence of a dis- continuity in the streamfunction field at infinity which is related to the slow decay of this field. We demonstrate how this difficulty can be overcome by reformulating the problem using a suitable background ”skeleton” field expressed in terms of the corresponding Oseen flow combined with spectral filtering. The method is thoroughly validated for Reynolds numbers spanning two orders of magnitude with the re- sults comparing favourably against known theoretical predictions and the data available in the literature.
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The authors acknowledge the financial support from SHARCNET through a graduate scholarship and from the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Discovery Grant. Calculations were performed using the high-performance computing facilities provided by SHARCNET.
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J. Gustafsson, B. Protas, "Computation of Steady Incompressible Flows in Unbounded Domains," Computers and Fluids, v. 112 (2015) pp. 95-107
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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