Skip to main content
SpringerLink
Log in

A class of compact upwind TVD difference schemes

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

Abstract

A new method was proposed for constructing total variation diminishing (TVD) upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD (CTVD) schemes were tested, one is third-order accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a two-dimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.

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. Lele S K. Compact finite difference schemes with spectral-like resolution[J]. Journal of Computational Physics, 1992, 103(1):16–42.

    Article  MATH  MathSciNet  Google Scholar 

  2. Ravichandran K S. Higher order KFVS algorithms using compact upwind difference operators[J]. Journal of Computational Physics, 1997, 230(2):161–173.

    Article  Google Scholar 

  3. Tadmor E. Convenient total variation diminishing conditions for nonlinear difference schemes[J]. SIAM Journal on Numerical Analysis, 1988, 25(5):1002–1014.

    Article  MATH  MathSciNet  Google Scholar 

  4. Osher S. Riemann solvers, the entropy condition and difference approximations[J]. SIAM Journal on Numerical Analysis, 1984, 21(2):217–238.

    Article  MATH  MathSciNet  Google Scholar 

  5. Tu Guohua, Yuan Xiangjiang, Chen Lujun. A limited flux compact scheme suited to supersonic flows[J]. Acta Aeronautica et Astronautica Sinica, 2004, 25(4):327–332 (in Chinese).

    Google Scholar 

  6. Pirozzoli S. Conservative hybrid compact-WENO schemes for shock-turbulence interaction[J]. Journal of Computational Physics, 2002, 178(1):81–117.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1):202–228.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. China Aerodynamics Research and Development Center, Mianyang, 621000, Sichuan Province, P. R. China

    Tu Guo-hua  (涂国华) & Yuan Xiang-jiang Doctor  (袁湘江) (Professor)

  2. National CFD Laboratory, Beijing, 100083, P. R. China

    Tu Guo-hua  (涂国华) & Yuan Xiang-jiang Doctor  (袁湘江) (Professor)

  3. Center for Information Analysis, Research Institute of Chemical Defense, Beijing, 102205, P. R. China

    Xia Zhi-qiang  (夏治强)

  4. School of Software Engineering, Tongji University, Shanghai, 200331, P. R. China

    Hu Zhen  (呼振)

Authors
  1. Tu Guo-hua  (涂国华)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuan Xiang-jiang Doctor  (袁湘江)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xia Zhi-qiang  (夏治强)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hu Zhen  (呼振)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuan Xiang-jiang Doctor  (袁湘江).

Additional information

Communicated by LIN Jian-zhong

Project supported by the National Natural Science Foundation of China (Nos. 10172015 and 90205010)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tu, Gh., Yuan, Xj., Xia, Zq. et al. A class of compact upwind TVD difference schemes. Appl Math Mech 27, 765–772 (2006). https://doi.org/10.1007/s10483-006-0607-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-0607-1

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation