A semi-implicit finite volume model based upon staggered grid is presented for solving shallow water equation. The model employs a time-splitting scheme that uses a predictor-corrector method for the advection term. The fluxes are calculated based on a Riemann solver in the prediction step and a downwind scheme in the correction step. A simple TVD scheme is employed for shock capturing purposes in which the Minmond limiter is used for flux functions. As a consequence of using staggered grid, an ADI method is adopted for solving the discretized equations for 2-D problems. Several 1-D and 2-D flows have been modeled with satisfactory results when compared with analytical and experimental test cases. The model is also capable of simulating supercritical as well as subcritical flow.is the TVD-MacCormack method [5,9]. Most numerical methods belonging to these two classes utilize non-staggered grids [13].Staggered grids are often used for modeling subcritical 1-D, 2-D and 3-D hydrostatic currents [13]. Advantages of staggered grid-based methods include their efficiency for combination with ADI methods [14], as well as the fact that no special numerical methods need to be used to prevent the formation of checkered board fields which often arise in subcritical flow [15]. An interesting example of application of staggered-grid scheme in dam-break modeling is the work of Stelling and Duinmeijer in 2003 in which they used an implicit method for modeling of rapidly varied flow using conservation equations for energy, mass, and momentum [13].Recently, fractional methods have been used in modeling shallow water equations [16][17][18]. Time splitting is one of these methods that allows the solution of each term with a different scheme that suits best for that particular term; it is even possible to solve certain terms implicitly while solving other terms explicitly.Here, a finite volume method has been used for solving shallow water equations. The staggeredgrid scheme, which in spite of its advantages, remains still a new approach in the study of the dam-break phenomenon, has been used in this study in conjunction with the Godunov-type shock capturing method. In the present model, a simple shock capturing technique is used that was introduced by Zia and Banihashemi [12] for dam-break modeling. Time-splitting method is also utilized that allows for implicit-explicit solving procedure, which in turn makes it possible to use larger time steps as well as paving the ground to create an implicit link between a 1-D and a 2-D model in integrated 1-D-2-D models without needing to implicitly solve the entire terms of equations.
1-D GOVERNING EQUATIONS
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