Construction And Application Of Parallel Method With High Accuracy Scheme For Convection Diffusion Equation Of Pollutants

In the emergency decision-maling of pollution accidents,the numerical prediction of pollutant concentration with time and space distribution by using the concentration of convection diffusion equation is one of the most important parts.In order to accurate the emergency response and have precise decision,High precision and fast speed are required in the calculation process.It is necessary to construct a high-precision parallel method to achieve the purpose of both speed and accuracy.In order to In order to solve the above problems.In order to solve the above problems,the content of this article is as follows:In the first part of the article,we firstly discretized the concentration convection-diffusion equation with high accuracy,constructed a two-layer eight-point implicit format for the interior points,and then constructed a boundary layer difference format that matches the accuracy of the interior point format.Then Taylor expand the corresponding order for its time and space terms,and obtain the difference coefficients of the difference format using the undetermined coefficient method to obtain the time third order of the interior points and boundaries of the concentration convection diffusion' equation,and the 'spatial sixth order precision implicit difference format.Furthermore,we use the Von Neumann method to test stability analysis on the constructed difference scheme,and then verify the corresponding numerical example.Finally,it is proved that all the formats constructed in this paper meet the accuracy requirements of the third order in time and the sixth order in space,and are stable under certain conditions,and have a wide stability range.Within a certain range,the convection-dominated diffusion equation with a large convection coefficient can be calculated with the formats constructed in this paper.The second part of the article first proposes a new parallel computing method for the obtained tridiagonal equations based on the high-precision difference scheme constructed in Chapter one.On the basis of parallel processing,group intersections can also form a 2*2 block tridiagonal equation,it can be calculated in parallel again with the method,making the overall parallel computing quicker.Numerical examples show that it is good for multiprocessing or multiprocessor implementations.While maintaining the high precision of the solution,achieved great parallel effect.Therefore,the parallel method proposed in this paper is suitable for parallel calculation of convection-diffusion equations in two-dimensional or even higher dimensions.Taking the numerical solution of two-dimensional convection-diffusion equation as an example,we analysis the calculation time and efficiency of this method and serial method.The third part of the article deeply analyzed the effects of cycle time,calculation scale,and communication time on the overall computational acceleration.Propose effective methods to improve the parallel efficiency of MATLAB.By adopting the method of memory mapping,it can efficiently access large data sets on the disk that are too large to be kept in memory or take too long to load,which solves the problem that the data communication time of a large matrix affects the overall calculation speed.Using MEX hybrid compilation and MATLAB's extended features,combined with the language features of C language,the large-scale loop calculation in the calculation is completed using C/C++and MATLAB hybrid compilation.Numerical examples show that these are flexible for multiprocessor implementations,without changing the overall structure of the program,it can increase parallelism efficiency up to 400%.The fourth part of the article gives the application of the high-precision difference scheme constructed in this paper to practical environmental problems.The upstream oil boom is used as the first type of fixed boundary,and the downstream oil collection device is used as the first type of moving boundary to simulate the treatment process of river spillage accidents.By adopting the high-precision difference format of the one-dimensional concentration convection-diffusion equation constructed in this paper,the oil spill concentration changes when the oil boom and the oil recovery device are used as treatment devices are numerically simulated.