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標題: 用特徵裁縫有限點法解對流佔優的擴散對流反應問題
Characteristic tailored finite point method for convection-dominated convection-diffusion-reaction problems
作者: 張友友
Chang, Yo-Yo
關鍵字: 特徵裁縫有限點法;Characteristic tailored finite point method;擴散對流反應方程;對流占優;邊界層;內部層;convection-diffusion-reaction problems;convection-dominated;boundary layers;interbal layers
出版社: 應用數學系所
引用: [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.

In 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.
其他識別: U0005-1207201015210700
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