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Mathematical Problems in Engineering
Volume 2014, Article ID 257915, 15 pages
http://dx.doi.org/10.1155/2014/257915
Research Article

Development of a Cell-Centered Godunov-Type Finite Volume Model for Shallow Water Flow Based on Unstructured Mesh

1Institute of Hydraulic Structures and Water Environment, Zhejiang University, Hangzhou 310058, China
2Institute of Physical Oceanography, Ocean College, Zhejiang University, Hangzhou 310058, China
3State Key Laboratory of Satellite Ocean Environment Dynamics, The Second Institute of Oceanography, Hangzhou 310012, China

Received 6 December 2013; Accepted 15 April 2014; Published 28 May 2014

Academic Editor: Yonghong Wu

Copyright © 2014 Gangfeng Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based on the Godunov-type cell-centered finite volume method, this paper presents a two-dimensional well-balanced shallow water model for simulating flows over arbitrary topography with wetting and drying. The central upwind scheme is used for the computation of mass and momentum fluxes on interface. The novel aspect of the present model is a robust and accurate nonnegative water depth reconstruction method which is implemented in the unstructured mesh to achieve second-order accuracy in space and to track the moving wet/dry fronts of the flow over irregular terrain. By defining the bed elevation and primary flow variables at the cell center in the nonstaggered grid system, all computational cells are either fully wet or dry to avoid the problem of being partially wetted. The developed model is capable of being well balanced and preserving the computed water depth to be nonnegative under a certain CFL restriction, which makes it robust and stable. The present model is validated against three benchmark tests and two laboratory dam-break cases. Finally, the good agreement between the numerical results by the established model and measured data of the Malpasset dam break event on a 1/400 scale physical model demonstrates the capability of the model for the real-life applications.