Differential Quadrature Method for Flood Routing Using Diffusion Wave Model

Abstract

The flooding event occurs when the discharge of a river is more than the river capacity. With high and rough topographic structure, Turkey is located in a semi-arid climate zone and both spatial and seasonal distribution of precipitation is quite irregular. These irregular precipitations create the flooding events with landform, topographic structure, faulty land use, unplanned urbanization and destruction of forest areas. Since floods are characterized by discharge velocity, discharge level and high water levels, these flood characteristics should be known and preventive actions must be taken for all buildings to be built in river basins. The solutions which are made for determining flood characteristics are called as flood routing and developed by means of St. Venant equations. St. Venant equations can be solved in different wave approaches and named hydraulic methods in flood routing phenomenon. In addition to hydraulic methods, hydrological methods that based only mass conservation can also be used in flood routing phenomenon. St. Venant equations can be linearized mathematically with some assumptions, however different wave approaches can be used, it can be denoted as diffusion wave approach. The diffusion wave equation can be solved by different methods like finite difference and finite element methods. In this study, the differential quadrature method (DQM) is used for the numerical solution of diffusion wave equation and it is employed to real flood events data obtained from Sivapalan(1997) and Ozdogan(2010). The DQM results are compared with finite difference results [1,2]. As seen from the examples, for the solution in DQM it is enough to use fewer solution points.