Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

Binder, Benjamin J., Blyth, Mark G., & McCue, Scott W. (2013) Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions. IMA Journal of Applied Mathematics, 78(4), pp. 685-696.

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Abstract

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

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8 citations in Web of Science®

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ID Code: 58567
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: free-surface flow, flow over bottom topography, conformal mapping, boundary integral method, potential flow, wave-free flows
DOI: 10.1093/imamat/hxt015
ISSN: 0272-4960
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Oxford University Press
Copyright Statement: Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Deposited On: 21 Mar 2013 23:23
Last Modified: 05 May 2014 08:34

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