Several Kinds Of Alternating Group Difference Schemes Of Convection Diffusion

Convection diffusion equation is to describe some physical phenomena of fluidmotion.t is a kind of very important partial differential equation. It has very importantapplications in such aspects as heat conduction, seepage mechanics and particlediffusion. So the research of the numerical solution has important practical significance.But at this stage with the high speed development of high performance parallel computer,the important part of the partial differential equation numerical solution is the parallelfinite difference method.In the first chapter, we analysis the research significance, the research status and thedevelopment trend of the parallel difference scheme of convection diffusion equation athome and abroad. In the second chapter, a new alternating segment explicit-implicitmethod for the numerical solution of the convection diffusion equation is derived byexponential transform. The method has the obvious property of parallelism and isunconditionally stable. A numerical example is given which illustrates that the error ofthe present method is smaller than the classical alternating segment explicit-implicitmethod. Besides, the solution can be calculated when the coefficient b is very small. Inthe third chapter, based on high levels of explicit and implicit difference schemes fourasymmetric formats are established. Then according to the alternating segment explicitimplicit thoughts, a new alternating segment explicit implicit format is constructedbased on six difference schemes. And we also prove that this method is unconditionallystable. By compared with ASCN format, results show that the format has thecharacteristics of fast convergence speed. In the fourth chapter, based on the classicalCrank-Nicolson difference scheme, we construct the eight asymmetric formats whichapproach the convection diffusion equation. By using different difference scheme alternately at different temporal layer, we construct alternating segment explicit method.And we also prove that this method is unconditionally stable. Finally, compared withAGE-4P the operation results show that the order of convergence in this paper ishigher.