Analytical Solution of Nonlinear Diffusion Wave Model

AbstractThe Saint Venant equations are the equations governing open channel flow when a flood propagates. To obtain an analytical solution, the Saint Venant equations are approximately transformed to a nonlinear diffusion equation. The numerical result of the nonlinear diffusion equation explains the nonlinearity of the open channel flow and overland flow and the resulting asymmetry of the water surface profile. When the Saint Venant equations are numerically applied to flood routing in a finite region and finite time, a downstream boundary condition is necessary. Analytical solution of the appropriate nonlinear diffusion equation does not require the downstream boundary condition. The numerical result of the analytical solution of the approximate nonlinear diffusion equation is found to be suitable for simulation of the original nonlinear differential equation and the Saint Venant equations. The linearized diffusion model is found to be restricted in practical applications, and it cannot express nonlinea...