Efficiency and performances of finite difference schemes in the solution of saint Venant's equation

The computation of unsteady free-surface flows is required to estimate the arrival time and height of a flood waves at any downstream location in a river flow. The governing equations solved in this regards are the St. Venant equations. These equations are highly non-linear partial deferential equation and closed form solutions are not available except in very simplified one dimensional case. The computer revolution in twentieth century made a new era where numeric methods can be utilized effectively to solve nonlinear partial differential equations. Though several numerical schemes have been developed by various investigators for solving these equations, the choosing of efficient scheme regarding its efficiency, accuracy and computational effort has always been remaining as an important topic from very beginning. In this paper mainly results of two different schemes, Lax diffusive scheme and Beam and warming scheme are presented. Validations of the models were achieved by comparing their results with results of MIKE21C modeling tool. The results in terms of surface profiles at different times and velocity vectors for both the schemes when plotted, it was observed that both the schemes lead to same results. But in case of the Beam and Warming scheme, it was observed that it takes a very large computational time for simulation.