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A New Difference Scheme For Steady Convection-diffusion Equation

Posted on:2009-01-25Degree:MasterType:Thesis
Country:ChinaCandidate:B Y WangFull Text:PDF
GTID:2190360308979770Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
The physical process going with the matter transmiting and molecule diffusing and the flow of glutinous liquid, their mathematical models are ususlly the problems of the convection-diffusion equations with the stable solution that can be described the distribution of the polluted matter in the rivers pollution, air pollution, and nucleus rubbish pollution, are also described the physical phenomenon of the flow and the heated methods in the liquid and so on, so the research on the numerical methods of convection-diffusion equations have theoretical and pratical significance.There are some numerical methods of solving convection-diffusion equations, such as finit difference method, finit element method, and finit volume method and so on. However, when the convection item is dominated in the convection-diffusion equations, the equations take on the characteristics of hyperbola equations, in this case, the upwind domino offect that derived from the anisomerous convection item in the convection-diffusion equations makes it more difficult to solve convection-diffusion equations, and the traditional difference method and standard Galerkin finit element method will generate the numerial oscillation, although upwind difference scheme can eliminate the oscillative phenomenon caused by anisomerous convection item, but it reflects the solution excessively, and leads to the diffusion of the solution. Recent years, most of people are apted to some nonstandard finit element and finit difference methods, such as upwind finit element method, characteristic finit element method, streamline-diffusion finit element method, characteristic difference method, generalized difference method and finit volume method.Considering 'the upwind domino effect' caused by the anisomerous convection item in the convection-diffusion equations, in this paper, starting frome the original convection-diffusion equation, it is changed into a conservative diffusion equation through the exponent transform, then the conservative diffusion equation is discreted by using the finit volume method, finally a new difference scheme is established. In this paper, the error estimate for one dimensional difference solution is given using the energy method, while maximum principle method, generalized difference method and energy estimate method are adapted to analyze the error for two dimensional difference solution, then numerical solutions for some instances are presented. The results show that the precision and astringency of difference schemes are satisfying, meanwhile the difference solutions haven't appeared the vibration and diffusion.
Keywords/Search Tags:convection-diffusion equation, exponent transform, finit volume method, error estimate, numerical instances
PDF Full Text Request
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