Stochastic Solution for Uncertainty Propagation in Nonlinear Shallow-Water Equations
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 12
Abstract
This paper presents a stochastic approach to describe input uncertainties and their propagation through the nonlinear shallow-water equations. The formulation builds on a finite-volume model with a Godunov-type scheme for its shock capturing capabilities. Orthogonal polynomials from the Askey scheme provide expansion of the variables in terms of a finite number of modes from which the mean and higher-order moments of the distribution can be derived. The orthogonal property of the polynomials allows the use of a Galerkin projection to derive separate equations for the individual modes. Implementation of the polynomial chaos expansion and its nonintrusive counterpart determines the modal contributions from the resulting system of equations. Examples of long-wave transformation over a submerged hump illustrate the stochastic approach with uncertainties represented by Gaussian distribution. Additional results demonstrate the applicability of the approach with other distributions as well. The stochastic solution agrees well with the results from the Monte Carlo method, but at a small fraction of its computing cost.
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Acknowledgments
The research work described in this paper is supported by the Office of Naval Research through Grant No. N00014-02-1-0903. The writers are appreciative of the three anonymous reviewers for their comments and suggestions and to Dr. David L. George for providing the finite-volume source code used in the present study. This is SOEST Contribution 7467.
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Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 12 • December 2008
Pages: 1732 - 1743
Copyright
© 2008 ASCE.
History
Received: Aug 24, 2007
Accepted: Jun 10, 2008
Published online: Dec 1, 2008
Published in print: Dec 2008
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