Development and Testing of 2D Finite Difference Model in Open Channels
- 169 Downloads
This study develops a depth-averaged two-dimensional (2D) numerical model using a finite difference method (FDM) on a staggered grid. The governing equations were solved using the Marker and Cell method that was developed at the Los Alamos laboratories by Harlow and Welch in 1965. In the paper, an explicit FDM was used to solve the governing equations. A first-order approximation was used for the temporal derivative. Second-order central difference approximations were used for space discretization. The time step is limited by the Courant–Friedrichs–Lewy (CFL) condition. The time step used in this study depends on the grid spacing and velocity components in the x- and y-directions. The study is divided into two steps: the first step is to develop a depth-averaged 2D numerical model to simulate the flow process. The second constructs a module to calculate the bed load transport and simulate the river morphology in the areas that have steep slopes, torrents, and mountain rivers. Developed model was applied to the artificial channel and a flood event in the Asungjun River section of the mountainous Yangyang Namdae River (South Korea). General simulation results showed that the developed model was in good agreement with the observed data.
KeywordsNumerical model Finite difference Staggered grid Depth-averaged Open channels
An important part of this work was realized during the author’s 3-year tenure at the Gangneung-Wonju National University, South Korea. The study was supported by the Institute for Disaster Prevention, Gangneung-Wonju National University, South Korea.
- 3.MacDonald, I. (1996). Analysis and computation of steady open channel flow. U. K: Dissertation, University of Reading.Google Scholar
- 7.Jia, Y., & Wang, S. S. Y. (2001). CCHE2D: two-dimensional hydrodynamic and sediment transport model for unsteady open channel flows over loose bed. Technical Rep. No. NCCHE-TR-2001-1. Oxford: School of Engineering, Univ. of Mississippi.Google Scholar
- 10.Horritt, M. (2004). Development and testing of a simple 2D finite volume model of sub critical shallow water flow. Journal of Numerical Mathematics, 44, 1231–1255.Google Scholar
- 15.Ahmadi, M. M., Ayyoubzadeh, S. A., Namin, M. M., & Samani, J. M. V. (2009). A 2D numerical depth-averaged model for unsteady flow in open channel bends. Journal of Agricultural Science and Technology, 11, 457–468.Google Scholar
- 19.Chow, V. T., & Zvi, A. B. (1973). Hydrodynamic modeling of two-dimensional watershed flow. Journal of the Hydraulics Division, 99(11), 2023–2040.Google Scholar
- 20.Bellos, C., Hrissanthou, V. (2003). Numerical simulation of morphological changes in rivers and reservoirs. Computers & Mathematics with Applications, 45, 453-467.Google Scholar
- 23.Dang, T. A. (2013). Development of two dimensional riverbed variation model in mountainous rivers. South Korea: Dissertation Gangneung-Wonju National University.Google Scholar
- 25.Hoffmann, K. A., Chiang, S. T., (2000). Computational fluid dynamics. Volume 1, fourth edition. http://www.eesbooks.com/booklist.html.
- 26.Matyka, M. (2004). Solution to 2D incompressible Navier–Stokes equations with SIMPLE, SIMPLER and Vorticity stream function approaches driven lid cavity problem: solution and visualization. Poland: University of Wrocław.Google Scholar