Comparison of solutions of Saint-Venant equations by characteristics and finite difference methods for unsteady flow analysis in open channel

摘要

The unsteady flow can be analysed by Saint-Venant equations. These equations can be solved by characteristics and finite difference methods. The Saint-Venant equations are changed into four complete differential equations in characteristics method and these equations are solved by drawing two characteristics lines. The Saint-Venant equations are changed into set nonlinear equations and are solved using Preissman scheme in finite difference method. This set of equation is changed into linear equation using Newton-Rafson method and can be solved using Sparce method. In this research, the results of the two method were compared and this was shown that: 1) these two methods can draw the surface profiles and flow hydrograph as well; 2) the finite difference method is more accurate than that one; 3) the mesh size in finite difference method can be larger than that one; 4) the difference between two methods are increased by increasing the time and distance.