Numerical simulation of free surface flow using lax diffusive explicit scheme

Abstract

In an open channel or overland flow of shallow depth, flood wave propagation is the concept which requires governing equations for its solution. The computation of governing equations (both momentum equation and continuity equations) to be solved are generally called the Saint-Venant equations. These equations are highly nonlinear partial differential equations, the solutions of which are very much complex. Numerical approaches are generally employed to solve these equations and proper discretization with proper selection of grid size and time step provides the results more effectively and accurately. In the present research work the Saint –Venant equations are solved through the lax diffusive explicit finite difference scheme. In this the characteristic equations are simultaneously solved in both boundaries for dynamic wave, which leads to give very accurate result. Two types of downstream boundary conditions were considered together with the condition of discharge hydrograph at upstream end. The physical laws which govern two basic principles in the hydraulics of flow of water are principle of conservation of mass and principle of conservation of momentum. These two laws are of mathematical form generally expressed in partial differential equation form known as Saint-Venant equations. Conversion of these equations into ordinary partial differential equation forms and the simple discretization of this equation by explicit scheme using CFD tool are presented in this paper.