Research Article Development of a Cell-Centered Godunov-Type Finite Volume Model for Shallow Water Flow Based on Unstructured Mesh Gangfeng Wu, 1 Zhiguo He, 2,3 and Guohua Liu 1 1 Institute of Hydraulic Structures and Water Environment, Zhejiang University, Hangzhou 310058, China 2 Institute of Physical Oceanography, Ocean College, Zhejiang University, Hangzhou 310058, China 3 State Key Laboratory of Satellite Ocean Environment Dynamics, he Second Institute of Oceanography, Hangzhou 310012, China Correspondence should be addressed to Zhiguo He; hezhiguo@zju.edu.cn Received 6 December 2013; Accepted 15 April 2014; Published 28 May 2014 Academic Editor: Yonghong Wu Copyright © 2014 Gangfeng Wu et al. his 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. Based on the Godunov-type cell-centered inite volume method, this paper presents a two-dimensional well-balanced shallow water model for simulating lows over arbitrary topography with wetting and drying. he central upwind scheme is used for the computation of mass and momentum luxes on interface. he 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 low over irregular terrain. By deining the bed elevation and primary low 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. he 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. he 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. 1. Introduction he two-dimensional (2D) shallow water equations (SWEs) have been widely used to mathematically describe free surface lows over complex topography, such as river and overland lows, dam-break loods, and estuarine and coastal circula- tion. Because the exact analytical solutions of SWEs are only available for some simple and speciic cases, it is important to develop numerical methods of SWEs with good properties for general applications in hydraulic and coastal engineering. Various numerical methods have been developed to obtain the satisfactory solutions of SWEs, such as the inite difer- ence [1, 2], the inite volume [3–6], and lattice Boltzmann methods [7]. he inite volume method, which can provide solutions with good mass and momentum conservations in both structured and unstructured computational meshes, is probably the most popular numerical technique to solve SWEs. In recent decades, Godunov-type cell-centered inite vol- ume schemes have been applied to solve SWEs numerically due to its robustness [8–16]. By considering the mesh element as the control volume, Godunov-type schemes can reasonably simulate the most complicated low phenomena including lows with mix regimes and shock-wave discontinuities [9]. However, when modeling the lows over arbitrary topography in realistic engineering applications, there are still challenges of handling the wetting and/or drying moving boundaries and preserving the well-balanced property [17]. Several mathematical and numerical treatments have been proposed to preserve the “lake at rest” steady states, which are known as well-balanced property [17] or C- property [18]. For example, Berm´ udez and Vazquez [18] proposed an upwind discretization method to balance the numerical luxes and the bed slope source terms. In com- parison with earlier models that used the the centred dis- cretization method, this technique signiicantly improved Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 257915, 15 pages http://dx.doi.org/10.1155/2014/257915