A series-solution method for free-boundary problems arising from flow over topography

Higgins, P.J., Read, W.W., and Belward, S.R. (2006) A series-solution method for free-boundary problems arising from flow over topography. Journal of Engineering Mathematics, 54 (4). pp. 345-358.

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An analytical series method is presented for steady, two-dimensional, irrotational flow of a single layer of constant-density fluid over topography. This problem is formulated as a Laplacian free-boundary problem with fully nonlinear boundary conditions. The method is an iterative scheme that allows the calculation of analytical series solutions for supercritical, transcritical and subcritical flow regimes over arbitrary topography. By an appropriate choice of the free-boundary representation, exponential convergence of the series solution is achieved. With this accuracy, the issue of apparent dual transcritical/subcritical solutions previously obtained by boundary-integral-equation methods (BIEM) is resolved. Results are compared with solutions previously obtained using BIEM, and solutions are presented for flow over asymmetric and arbitrarily shaped obstacles.

Item ID: 4032
Item Type: Article (Research - C1)
ISSN: 1573-2703
Keywords: analytical series; arbitrary topography; exponential convergence; nonlinear solutions
Date Deposited: 12 Nov 2009 23:46
FoR Codes: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics @ 50%
01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 75%
97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 25%
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