Characteristic Tailored Finite Point Method for Convection-Dominated Convection-Diffusion-Reaction Problems

In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient th...

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Published inJournal of scientific computing Vol. 47; no. 2; pp. 198 - 215
Main Authors Shih, Yintzer, Kellogg, R. Bruce, Chang, Yoyo
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2011
Springer Nature B.V
Subjects
Algorithms
Boundary layer
Boundary layers
Computation
Computational Mathematics and Numerical Analysis
Construction
Convection-diffusion equation
Diffusion coefficient
Diffusion layers
Finite element method
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Reaction-diffusion equations
Theoretical
Tailored finite point
Internal layer
Convection-diffusion-reaction
Characteristic
Finite element
Boundary layer
Online AccessGet full text
ISSN0885-7474
1573-7691
DOI10.1007/s10915-010-9433-7

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Abstract In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers regardless the mesh size, and depicts that CTFPM method with a streamline grid has excellent performance compared with the tailored finite point method and a streamline upwind finite element method when ε is small.
AbstractList In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers regardless the mesh size, and depicts that CTFPM method with a streamline grid has excellent performance compared with the tailored finite point method and a streamline upwind finite element method when Delta *e is small.
In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers regardless the mesh size, and depicts that CTFPM method with a streamline grid has excellent performance compared with the tailored finite point method and a streamline upwind finite element method when ε is small.
In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers regardless the mesh size, and depicts that CTFPM method with a streamline grid has excellent performance compared with the tailored finite point method and a streamline upwind finite element method when ε is small.
Author Chang, Yoyo
Kellogg, R. Bruce
Shih, Yintzer
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  surname: Shih
  fullname: Shih, Yintzer
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  organization: Department of Applied Mathematics, National Chung Hsing University
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  givenname: R. Bruce
  surname: Kellogg
  fullname: Kellogg, R. Bruce
  organization: Department of Mathematics, University of South Carolina
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  givenname: Yoyo
  surname: Chang
  fullname: Chang, Yoyo
  organization: Department of Applied Mathematics, National Chung Hsing University
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crossref_primary_10_1016_j_camwa_2013_03_017
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Cites_doi 10.1016/0045-7825(82)90071-8
10.1007/s10915-008-9187-7
10.1007/BFb0069940
10.1007/s10915-009-9292-2
10.1007/s10915-010-9354-5
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Internal layer
Convection-diffusion-reaction
Characteristic
Finite element
Boundary layer
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Digital Library of Mathematical Functions. 2010-05-07. National Institute of Standards and Technology from http://dlmf.nist.gov
HanH.HuangZ.Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensionsJ. Sci. Comput.20094120022010.1007/s10915-009-9292-21203.652252550367
HanH.HuangZ.KelloggR.B.A tailored finite point method for a singular perturbation problem on an unbounded domainJ. Sci. Comput.20083624326110.1007/s10915-008-9187-71203.652212434846
HemkerP.W.HackbuschW.TrottenbergU.Mixed defect correction iteration for the accurate solution of convection diffusion equationMultigrid Methods1982BerlinSpringer48550110.1007/BFb0069940
ShihY.KelloggR.B.TsaiP.A tailored finite point method for convection-diffusion-reaction problemsJ. Sci. Comput.20104323926010.1007/s10915-010-9354-51203.651512607151
HanH.HuangZ.A tailored finite point method for the Helmholtz equation with high wave numbers in heterogeneous mediumJ. Comput. Math.2008267287391174.650482444729
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Y. Shih (9433_CR9) 2010; 43
H. Han (9433_CR4) 2009; 41
K.W. Morton (9433_CR8) 1996
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– reference: HanH.HuangZ.KelloggR.B.A tailored finite point method for a singular perturbation problem on an unbounded domainJ. Sci. Comput.20083624326110.1007/s10915-008-9187-71203.652212434846
– reference: Digital Library of Mathematical Functions. 2010-05-07. National Institute of Standards and Technology from http://dlmf.nist.gov/
– reference: HanH.HuangZ.Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensionsJ. Sci. Comput.20094120022010.1007/s10915-009-9292-21203.652252550367
– reference: HanH.HuangZ.A tailored finite point method for the Helmholtz equation with high wave numbers in heterogeneous mediumJ. Comput. Math.2008267287391174.650482444729
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– reference: MortonK.W.Numerical Solution of Convection-Diffusion Problems1996LondonChapman & Hall0861.65070
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SubjectTerms Algorithms
Boundary layer
Boundary layers
Computation
Computational Mathematics and Numerical Analysis
Construction
Convection-diffusion equation
Diffusion coefficient
Diffusion layers
Finite element method
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Reaction-diffusion equations
Theoretical
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Title Characteristic Tailored Finite Point Method for Convection-Dominated Convection-Diffusion-Reaction Problems
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