Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Digital Library of Mathematical Functions. 2010-05-07. National Institute of Standards and Technology from http://dlmf.nist.gov/

  2. Han, H., Huang, Z., Kellogg, R.B.: The tailored finite point method and a problem of P. Hemker. In: Proceedings of the International Conference on Boundary and Interior Layers—Computational and Asymptotic Methods, Limerick, July 2008

  3. Han, H., Huang, Z., Kellogg, R.B.: A tailored finite point method for a singular perturbation problem on an unbounded domain. J. Sci. Comput. 36, 243–261 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Han, H., Huang, Z.: Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensions. J. Sci. Comput. 41, 200–220 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Han, H., Huang, Z.: A tailored finite point method for the Helmholtz equation with high wave numbers in heterogeneous medium. J. Comput. Math. 26, 728–739 (2008)

    MATH  MathSciNet  Google Scholar 

  6. Hemker, P.W.: Mixed defect correction iteration for the accurate solution of convection diffusion equation. In: Hackbusch, W., Trottenberg, U. (eds.) Multigrid Methods, pp. 485–501. Springer, Berlin (1982)

    Chapter  Google Scholar 

  7. Hughes, T.J.R., Brooks, A.N.: Streamline upwind Petrov-Galerkin formulations for convection-dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199–259 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  8. Morton, K.W.: Numerical Solution of Convection-Diffusion Problems. Chapman & Hall, London (1996)

    MATH  Google Scholar 

  9. Shih, Y., Kellogg, R.B., Tsai, P.: A tailored finite point method for convection-diffusion-reaction problems. J. Sci. Comput. 43, 239–260 (2010)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, National Chung Hsing University, Taichung, 402, Taiwan

    Yintzer Shih & Yoyo Chang

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    R. Bruce Kellogg

Authors
  1. Yintzer Shih
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Bruce Kellogg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoyo Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yintzer Shih.

Additional information

Supported by the National Science Council of Taiwan through Project NSC 99-2115-M-005-003.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shih, Y., Kellogg, R.B. & Chang, Y. Characteristic Tailored Finite Point Method for Convection-Dominated Convection-Diffusion-Reaction Problems. J Sci Comput 47, 198–215 (2011). https://doi.org/10.1007/s10915-010-9433-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-010-9433-7

Keywords

Search

Navigation