Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18178
DC FieldValueLanguage
dc.contributor簡澄陞zh_TW
dc.contributor洪子倫zh_TW
dc.contributor.advisor施因澤zh_TW
dc.contributor.advisorYin-Tzer Shihen_US
dc.contributor.author張友友zh_TW
dc.contributor.authorChang, Yo-Yoen_US
dc.contributor.other中興大學zh_TW
dc.date2011zh_TW
dc.date.accessioned2014-06-06T07:03:01Z-
dc.date.available2014-06-06T07:03:01Z-
dc.identifierU0005-1207201015210700zh_TW
dc.identifier.citation[1] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, 1964. [2] H. Han, Z. Huang and R.B. Kellogg,” The tailored finite point method and a problem of P. Hemker, Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008. [3] H. Han, Z. Huang and R.B. Kellogg,” A tailored finite point method for a singular perturbation problem on an unbounded domain, J.Sci. Comp., 36 (2008), pp. 243-261. [4] H. Han and Z. Huang,” Tailored Finite Point Method for a Singular Perturbation Problem with Variable Coefficients in Two Dimensions, J.Sci. Comp., 41 (2009), pp. 200-220. [5] H. Han and Z. Huang, A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium, J. Comp. Math., 26 (2008), pp. 728-739. [6] P.W. Hemker, Mixed defect correction iteration for the accurate solution of convection diffusion equation, Multigrid Methods, W. Hackbusch and U. Trottenberg, eds., Berlin Springer, (1982), pp. 485-501. [7] T.J.R. Hughes and A.N. Brooks, Streamline upwind petrov-galerkin formulations for convection-dominated flows with particular emphasis on the incompressible navier-stokes equations. Comput.Methods Appl. Mech. Engrg., 32 (1982), pp. 199-259. [8] K.W. Morton, Numerical Solution of Convection-Diffusion Problems, Chapman & Hall, London, (1996). [9] Y. Shih, R.B. Kellogg and P. Tsai, ” A Tailored Finite Point Method for Convection-Diffusion-Reaction Problems, J. of Sci. Compu., 43 (2010), pp. 239-260.zh_TW
dc.identifier.urihttp://hdl.handle.net/11455/18178-
dc.description.abstract在這篇論文中,我們使用了特徵裁縫有限點法來處理擁有變數對流係數的擴散對流反應問題。我們的數值結果主要針對的是擴散較小的情形,同時也看得出在擁有邊界斷層或是內部斷層的問題中,在我們所建立的網格上的特徵裁縫有限點法,其結果比裁縫有限點法以及一些知名的有限單元法來得更完美。zh_TW
dc.description.abstractIn this thesis, we propose a characteristic tailored finite point method (CTFPM) in solving the convection-diffusion-reaction equation with variable convection coefficients. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers in size of O(epsilon) regardless the mesh size, and depicts that CTFPM method in the streamline grid has excellent performance in comparing with tailored finite point method and some well-known finite element methods when epsilon is small.en_US
dc.description.tableofcontentsContents 1 Introduction 1 2 Characteristics and streamline-aligned grid generation 2 2.1 Solution decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Algorithm for generating the streamline-aligned grid . . . . . . . . . . . . . . 3 3 Characteristics tailored finite point method 6 3.1 The characteristic tailored finite point method . . . . . . . . . . . . . . . . . 6 3.2 Truncation error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Numerical Experiments 14 4.1 Problem 1. Homogeneous problem with variable velocity field . . . . . . . . 14 4.2 Problem 2. Homogeneous semicircular flow problem . . . . . . . . . . . . . . 16 4.3 Problem 3. Nonhomogeneous problem with exact smooth solution . . . . . . 17 4.4 Problem 4. Homogeneous variable velocity problem with numerical layers . . 22 Bibliography…..23zh_TW
dc.language.isoen_USzh_TW
dc.publisher應用數學系所zh_TW
dc.relation.urihttp://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1207201015210700en_US
dc.subject特徵裁縫有限點法zh_TW
dc.subjectCharacteristic tailored finite point methoden_US
dc.subject擴散對流反應方程zh_TW
dc.subject對流占優zh_TW
dc.subject邊界層zh_TW
dc.subject內部層zh_TW
dc.subjectconvection-diffusion-reaction problemsen_US
dc.subjectconvection-dominateden_US
dc.subjectboundary layersen_US
dc.subjectinterbal layersen_US
dc.title用特徵裁縫有限點法解對流佔優的擴散對流反應問題zh_TW
dc.titleCharacteristic tailored finite point method for convection-dominated convection-diffusion-reaction problemsen_US
dc.typeThesis and Dissertationzh_TW
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.languageiso639-1en_US-
item.grantfulltextnone-
item.cerifentitytypePublications-
item.openairetypeThesis and Dissertation-
item.fulltextno fulltext-
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