The Structure Of The High Precision Parallel About Concentration Convection Diffusion Equation And The Application

Convection diffusion equation plays a key role in the field of environment. For instance, we can use the equation to describe the distribution of pollutants in rivers, atmosphere and so on. Therefore, there is very important significance in the study of Convection diffusion equation methods. In the present computation of convection diffusion equation, finite difference method is one of important methods in numerous numerical solving methods. However, the stability of the explicit scheme of the method is limited. And the implicit scheme needs to solve large linear equation so it is difficult to be paralleled.With the rapid development of high performance computer, parallel algorithm is developing rapidly in recent years. And research at home and abroad scholars have made many research results. For example, Evans and Zhang bao-lin put forward a series of parallel algorithm in view of the diffusion equation and convection diffusion equation. But the accuracy of the some parallel algorithm is not high. As a result, it’s very necessary to construct parallel algorithm which has the high precision in order to improve the computing speed and accuracy. This article mainly constructed a kind of parallel algorithm for the one dimensional convection diffusion equation and the two dimensional convection diffusion equation. In addition, the two dimensional precision parallel algorithm is applied to the practical problems in the environment.In the second chapter of this article, a new class of parallel format is respectively constructed for the one dimensional and two dimensional diffusion equation and the one dimensional and two dimensional convection diffusion equation, which has the second order accuracy. Then, we respectively calculated each example and analyzed the results. Finally, the effectiveness of the format was verified.In the third chapter of this article, a new class of parallel format is respectively constructed for the one dimensional and two dimensional diffusion equation and the one dimensional convection diffusion equation, which has the higher order accuracy. Then, we respectively calculated each example and analyzed the numerical solution and exact solution. We found the two curve match perfectly and the calculation accuracy is significantly higher than the parallel format in the second chapter. Finally, the effectiveness of the format was verified.In the fourth chapter of this article, we studied the diffusion process of disinfectant after dropping in the aquaculture ponds based on the higher order accuracy parallel format about two dimensional diffusion equation. Considering the required total diffusion time and the total amount of the disinfectant, we concluded a more reasonable way. Thus, the research results can provide certain reference for pond aquaculture.