Skip to main content
SpringerLink
Log in

Numerical analysis and construction of limiter of high resolution difference scheme

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In the paper, based on the theory of the remainder effects of difference schemes, some typical limiters are analysed and compared. For different limiters, the different strength of numerical dissipation and dispersion of schemes is the reason why the schemes show obvious different characteristics. After analysing and comparing the numerical dissipation and dispersion of various schemes, a new kind of limiter is proposed. The new scheme has high resolution in sharp discontinuities, and avoids the “distortion” due to the stronger numerical dispersion in the relatively more smooth region. Numerical experiments show that the scheme has good properties.

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. B. Van Leer, Towards the ultimate conservative difference scheme, II. Monotonicity and conservation combined in a second order scheme,J. Comp. Phys.,14 (1974), 361–370.

    Article  MATH  Google Scholar 

  2. P. L. Roe, Numerical algorithms for the linear wave equation, Royal Aircraft Establishment Technical Report 81047 (1981).

  3. P. L. Roe, Some contributions to the modelling of discontinuous flows, inProceedings AMS-SLAM Sum, on Large-Scale Comp. in Fluid Mech., 1983, edited by B. E. Engquist et al.,Lectures in Appl. Math.,22, 2 (1985), 673.

  4. S. R. Chakravarthy and S. Osher, High resolution applications of the Osher upwind scheme for the Euler equations, AIAA paper presented at 6th CFD Conference (1983).

  5. P. K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws,SIAM J. Numer. Anal.,21, 5 (1984), 995–1011.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Harten, High resolution schemes for hyperbolic conservation laws.J. Comput. Phys.,49 (1983), 357–393.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Jameson, Positive schemes and shock modelling for compressible flows,Internat. J. for Numer. Methods Fluids,20 (1995), 743–770.

    Article  MATH  MathSciNet  Google Scholar 

  8. Liu Ruxun, The study of the remainder effects of FDS,J. Comput. Phys.,9, 4 (1992). 479, (in Chinese)

    Google Scholar 

  9. Liu Ruxun, The remainder-effect analysis of FDS and the applications to reforming or optimazing of FDS,J. of CUST,24, 3 (1994), 271, (in Chinese)

    Google Scholar 

  10. Liu Ruxun and Zhou Zhaohui, The remainder-effect analysis of FDS and the applications,Applied Mathematics and Mechanics (English Ed.),16, 1 (1995), 87–96.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, P.R. China

    Zhang Mengping & Liu Ruxun

Authors
  1. Zhang Mengping
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liu Ruxun
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Dai Shiqiang and Liu Ciqun

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mengping, Z., Ruxun, L. Numerical analysis and construction of limiter of high resolution difference scheme. Appl Math Mech 19, 677–686 (1998). https://doi.org/10.1007/BF02452376

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02452376

Key words

Search

Navigation