Development and Testing of 2D Finite Difference Model in Open Channels

Abstract

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.