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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 209562, 20 pages
Research Article

A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids

1School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2Hubei Key Laboratory of Digital Valley Science and Technology, Wuhan 430074, China
3Laboratory of Numerical Modeling Technique for Water Resources, Department of Water Resources and Environment, Pearl River Water Resources Research Institute, Guangzhou 510623, China

Received 16 February 2014; Revised 11 June 2014; Accepted 11 June 2014; Published 10 July 2014

Academic Editor: Hari M. Srivastava

Copyright © 2014 Sheng Bi 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.


A second-order accurate, Godunov-type upwind finite volume method on dynamic refinement grids is developed in this paper for solving shallow-water equations. The advantage of this grid system is that no data structure is needed to store the neighbor information, since neighbors are directly specified by simple algebraic relationships. The key ingredient of the scheme is the use of the prebalanced shallow-water equations together with a simple but effective method to track the wet/dry fronts. In addition, a second-order spatial accuracy in space and time is achieved using a two-step unsplit MUSCL-Hancock method and a weighted surface-depth gradient method (WSDM) which considers the local Froude number is proposed for water depths reconstruction. The friction terms are solved by a semi-implicit scheme that can effectively prevent computational instability from small depths and does not invert the direction of velocity components. Several benchmark tests and a dam-break flooding simulation over real topography cases are used for model testing and validation. Results show that the proposed model is accurate and robust and has advantages when it is applied to simulate flow with local complex topographic features or flow conditions and thus has bright prospects of field-scale application.