# Analytical series solutions for three-dimensional supercritical flow over topography

Higgins, P.J., Read, W.W., and Belward, S.R. (2012) Analytical series solutions for three-dimensional supercritical flow over topography. Journal of Engineering Mathematics, 77 (1). pp. 39-49. PDF (Published Version) - Published Version Restricted to Repository staff only
View at Publisher Website: http://dx.doi.org/10.1007/s10665-012-954...

## Abstract

An analytical series solution method for three-dimensional, supercritical flow over topography is presented. Steady, nonlinear solutions are calculated for a single layer of inviscid, constant-density fluid that flows irrotationally over an obstacle that varies significantly in the x-, y- and z-directions. Accurate series solutions for the free surface and a series of stream tubes throughout the flow region are calculated to demonstrate the three-dimensional properties of the problem. These solutions provide valuable insight into the three-dimensional interactions between the fluid and obstacle which is impossible to gain from any two-dimensional model. The model is described by a Laplacian free-boundary problem with fully nonlinear boundary conditions. The solution method consists of iteratively updating the location of the free surface (on top of the fluid) using a cost function which is derived from the Bernoulli equation. Root-mean-square errors in the boundary conditions are used as convergence criteria and a measure of the accuracy of the solution. This method has been used to solve the two-dimensional version of this problem in the past. Here, we detail the extensions required for three-dimensional flow.

Item ID: 23764 Article (Research - C1) 1573-2703 three-dimensional solutions; supercritical flow 01 Nov 2012 06:13 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics @ 75%01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations @ 25% 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100% Total: 7 More Statistics

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