NDLI: Analytical series solutions for three-dimensional supercritical flow over topography

Content Provider	Springer Nature Link
Author	Higgins, P. J. Read, W. W. Belward, S. R.
Copyright Year	2012
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.
Starting Page	39
Ending Page	49
Page Count	11
File Format	PDF
ISSN	00220833
Journal	Journal of Engineering Mathematics
Volume Number	77
Issue Number	1
e-ISSN	15732703
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-05-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Three-dimensional solutions Supercritical flow Mathematical Modeling and Industrial Mathematics Analysis Applications of Mathematics Mechanics Numeric Computing
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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