Structure Of High Precision Difference Scheme About Convection Diffusion Equation And The Application In Environment

In the reality of science and technology,most of the simulation problems can be solved by the convection diffusion equation.The concentration distribution of pollutants in water and in the atmosphere,and the behavior and fate can be also described by the concentration convection diffusion equation.So making a stable,effective and high-precision solving algorithm of the convection diffusion the equation has a very important theoretical and practical significance.At present,the numerical solutions commonly used are finite volume method,finite element method,finite analytic method and finite difference method.The finite difference method is used commonly in the field of engineering and scientific research,and the finite difference method becomes a hot topic for many scholars study,because it has the advantages of less involved grid points,high precision and so on.In this paper,two methods are used to construct the finite difference scheme with high accuracy.We analyze its stability with the Von Neumann and numerical calculations,then make it be applied to the environmental problems.Firstly,in the second chapter of the paper,we construct a three-high-accuracy difference scheme for the concentration diffusion equation and the concentration of the convection diffusion equation by the method of undetermined coefficients,its precision can be achieved O(?t4,?x8).We make numerical calculations by citing related numerical examples,compared numerical solution to the exact solutions,we find that the results are basically the same,and the error between the two can achieve the theoretical error.So it can be proved that the three layer difference scheme is effective,and it can also achieve the theoretical precision.Secondly,in the third chapter of the paper,the concentration on the first partial derivatives are discretized in time of the n+1/2 layer.The average value of n+1 and n time layer and the space of two order partial derivative shows the space for the n+1/2 layer for the two order partial derivatives.In order to make the space reach higher precision,the concentration in the space of the Taylor series expands.When the Taylor series expands to N,its precision can be achieved O(?t2,?xN).The numerical examples show that the structure of the two layer difference scheme is effective,and can reach the theoretical precision.Finally,in the fourth chapter of the article,we take the oil spilling for an example,we adopt the high accuracy difference scheme constructed in this paper to make a numerical simulation of oil concentration of change.Then we select the appropriate oil recovery rate according to the rated receiving amount per unit time from receiving device.