RBF-DQ Solution for Shallow Water Equations
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 139, Issue 1
Abstract
A mesh-free and highly convergent radial basis function–based differential quadrature method (RBF-DQ) is implemented to simulate shallow water waves in the marine environment and open channels. RBF-DQ is applicable in waterways of regular or irregular geometries for the simulation of currents and tidal waves. The multiquadric (MQ)-type radial basis function is used for the purpose of this study. MQ radial basis function has one or two shape parameters whose values significantly affect the accuracy of the results. To find appropriate values of the shape parameters, a parameter estimation methodology is introduced based on cross validation. The accuracy of RBF-DQ is evaluated by two idealized numerical examples along with a field application for the Oresund Strait located between Sweden and Denmark. In each case, either analytical, numerical solutions from other software programs or measured data were taken as benchmark solutions. Results of this study show that RBF-DQ, unlike conventional polynomial-based DQ, can be applied to irregular domains for tidal wave simulation. The method has two main advantages; first, it is mesh free and does not need mesh generation; second, with many fewer nodes, the results obtained compared well with analytical and benchmark solutions of other numerical schemes.
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Acknowledgments
The authors acknowledge Professor Simon Neill from the Center for Oceanography for providing POLCOMS results.
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Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 139 • Issue 1 • January 2013
Pages: 45 - 60
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 26, 2010
Accepted: May 23, 2012
Published online: May 26, 2012
Published in print: Jan 1, 2013
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