奇異攝動(dòng)問題的自適應(yīng)方法.pdf

1、湘潭大學(xué)碩士學(xué)位論文奇異攝動(dòng)問題的自適應(yīng)方法姓名：楊銀申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：黃云清20060428ABSTRACTAdaptive grid methods are becoming established as valuable computational tech-niques for numerical solution of differential equations with near-singular

2、solution. Adap-tive methods are equally effective in approximation solutions of problem with boundarylayers or interior layers. We mainly discuss adaptive redistributing mesh method, whichis called as moving mesh method.

3、The model of eddy viscosity and velocity distribution based on Prandtl MixingLength in turbulent pipe flow which is source of engineering problem is solved in thispaper. It is an optimal controlling problem. The mathemat

4、ical model is a nonlinearsingulary perturbed differential equation with boundary layer. We discretize this non-linear problem by using first- and second- order difference scheme including upwindscheme. We solve the discr

5、etized nonliner equations by Newton-Raphson method. Themesh is generated and moved by equidistributing principle to capture the boundarylayer. We design a iterative algorithm to solve the controlling problem. The numeric

6、alresult support our algorithm. Then, this paper shows how to apply the optimal meshbased on derivative error generated by interpolation function to adaptive finite methodand design a efficient adaptive algorithm to move

7、 mesh based on derivative error.Our discussion is partitioned into chapters on the following topics: In the firstchapter, we introduce the background and result of adaptive method; The second chap-ter, we solve the compl

8、icated engineering mathematical model in details; In the thirdchapter, we introduce the generation of optimal meshes for controlling the errors inderivative error for piecewise interpolation; In the forth chapter, we con

9、struct adaptivefinite method based on derivative error; In the fifth chapter, we have some error esti-mation and some convergence analyses; In the end, we draw a conclusion of this workand make some comments on the prosp