Differential Quadrature Method in Open Channel Flows: Aksu River, Turkey

Abstract

A diffusion wave equation, which is derived from the Saint-Venant equations for one-dimensional, gradually varied, unsteady open-channel flow, describes the wave propagation in open channels. Therefore, it is important to solve the diffusion wave equation accurately and efficiently. In this paper, a numerical solution for a diffusion wave equation is developed by using the Differential Quadrature Method (DQM). The performance of DQM is tested against two other numerical solution methods, the finite difference method (FDM) and finite volume method (FVM). In order to demonstrate the applicability of DQM, first a hypothetical example is solved with both DQM and the two other numerical methods. Then, the DQM is applied to a real flooding event that occurred in Aksu River, Sutculer Basin, located in Mediterranean Region, Turkey. The measured flow rates are routed through the Aksu River by the diffusion wave equation and the outflow is obtained by DQM. Finally, this flood event is also solved by explicit and implicit approximations of FDM and FVM, and the results are compared to the solution obtained by using DQM. Based on the comparison of the results, it is concluded that DQM provides results close to those obtained using FDM and FVM but with higher computational speed fewer nodes and less memory usage.