Numercial Simulation For Two Dimension Water Contamination Problem

In this paper the three-dimensional convection-diffusion problem is reduced to a manageable two-dimensional problem, equivalent to only consider the flat direction of the convection-diffusion without considering the vertical movement of material deposition. Using the fractional step method to two-dimensional convection-diffusion problem into two-dimensional diffusion problem and two-dimensional convection problem.P-R method is an alternating direction algorithm,this method has the na-ture of unconditional stability in dealing with two-dimensional diffusion prob-lem.Drawback is that it only second-order accuracy, and can not be extended to three-dimensional case.The meaningful part of convection-diffusion equation is convection-dominated diffusion equation. For solving convection-dominated diffusion equation is mainly to solve the numerical simulation of convection part.Because low precision and more calculation steps of upwind scheme and Lax-Wendroff scheme with calcu-lating convection part,WENO scheme of S.Osher and Chi-wang Shu take Newton interpolation method and the stream fuction to solve Euler equation, the method has high precision in space and can effectively capture the shock wave.Taking into account the second order accuracy of diffusion calculation,this paper take WENO 3 points to calculate convection part.At last the purpose of using Strang method is to further reduce the error of fractional step method.The main work of this paper is to solve convection-diffusion equation with WENO scheme based on Runge-Kutta method and this method is feasible by numerical example.