5 th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran Implicit and Explicit Numerical Solution of Saint-Venent Equations for Simulating Flood Wave in Natural Rivers G. Akbari 1 , B. Firoozi 2 1- Assistant Professor, Department of Civil Engineering, University of Sistan and Baluchestan 2- Post Graduate. Student, Department of Civil Engineering, University of Sistan and Baluchestan gakbari@hamoon.usb.ac.ir behzad_frz@yahoo.com Abstract River flow predictions are needed in many water resources management. The beginning of the modern study of unsteady flow in open channels can be traced to the latter half of the nineteenth century when the French engineer Saint-Venant introduced the partial differential equations of continuity and momentum governing free surface flow in open channels. These equations are highly nonlinear and therefore do not have analytical solutions. The computer revolution in twentieth century made a new era where numeric methods can be utilized effectively to solve nonlinear partial differential equations. This paper presents the results of two different numerical methods, namely; Preissmann and Lax diffusive schemes for numerical solution of Saint-Venant equations that govern the propagation of flood wave, in natural rivers, with the objective of the better understanding of this propagation process. The results have shown that the hydraulic parameters play important game in the flood wave propagation. The results of these numerical solutions are compared with the HEC-RAS commercial computer model. Keywords: numerical flood routing, Saint-Venant equations, Priessmann, Lax, HEC-RAS 1. INTRODUCTION Understanding flood wave routing theory and solving the governing equations accurately is an important issue in hydrology and hydraulics. In unsteady open channel flows, the velocity and water depth change with time and longitudinal position. For one-dimensional applications, the relevant flow parameters (e.g. V and y) are functions of time and longitudinal distance. Flood wave propagation in overland and open channel flow may be described by the complete equations of motion for unsteady non uniform flow, known as the dynamic wave equations, first proposed by Saint-Venant in 1871[1]. These equations are nonlinear and therefore do not have analytical solutions. With the greatly improved speed and capacity of digital computers in recent years, dynamic routing models have been widely used for flood forecasting. The first major mathematical model of a river system was developed by J.J. Stoker for the Ohio and Mississippi systems. There have been numerous studies in the literature to solve the Saint-Venant equations by using different numerical techniques. In this research solution of the fully Saint-Venant equations through Lax diffusive explicit scheme and Preissmann implicit scheme for unsteady flow simulation in open channels is presented. 2. GOVERNING EQUATIONS The dynamic routing model is based on the dynamic wave theory of the Saint-Venant equations which consist of the continuity and momentum equations. For prismatic channels having no lateral inflow or outflow the continuity and momentum equations defined as[2]: (1) (Continuity equation)           (2) (Momentum equation)              