Construction And Application Of High Precision Schemes For Two-Dimensional Complex Boundary Concentration Convection-Diffusion Equation

The convection-diffusion equation is an important class of partial differential equations that can be used to predict environmental problems such as river pollution,air pollution,and distribution of pollutants in nuclear waste.Boundary conditions play a role in the prediction of environmental problems.The high-precision format of the existing numerical calculation methods is mainly for the first type of boundary conditions,while the study of complex boundaries has many time layers,high storage requirements and slow calculation speed..In this paper,the high-precision difference schemes of one-dimensional and two-dimensional convection-diffusion equations under complex boundary conditions are studied,and the three-diagonal matrix is used to solve the problem,which greatly improves the calculation speed.This paper is of great significance and research value for solving environmental problems.In this paper,the high-precision difference schemes of one-dimensional and two-dimensional concentration convection-diffusion equations under complex boundary conditions are constructed respectively.The high-precision format with boundary conditions is directly constructed.Taylor expansion to fourth-order precision is performed for each point,and the undetermined coefficient method is used to solve the problem.The corresponding format satisfies the accuracy of the boundary format and the high precision of the interior point format.At the same time,the high-precision difference scheme of two-dimensional concentration convection-diffusion equation is constructed,and the Von Neumann stability analysis is carried out for the one-dimensional and two-dimensional boundary difference formats and the two-dimensional high-precision difference scheme under normal eonditions,The results show that the three kinds of differences.The format is stable under certain conditions;then the numerical verification of the corresponding examples proves the validity of the format,which satisfies the accuracy requirements of the second-order time and the fourth-order space.It turns out that all the formats eonstructed in this paper are stable and effective.Finally,this paper takes the oil spill and the oil collection device to deal with the oil spill as an example.The high-precision differential format under the one-dimensional and two-dimensional complex boundary conditions constructed in this paper is used to simulate the oil-removing device to enclose the oil at a certain moving speed.The process of oil spill recovery in the range of intercepting oil spills and observing the change of oil concentration provides a theoretical basis for the treatment of oil spill pollution.