Skip to main content

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 29))

Abstract

Conservative shock capturing methods for the unsteady Euler equations are reviewed and it is shown that the concepts of entropy satisfaction and total variation diminution can be applied to the classical Lax-Wendroff scheme. For an associated scheme to be efficient in applications, it is necessary that it be able to capture strong shock waves with high resolution. We describe a scheme which is efficient in both respects.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. A. Harten, “High resolution schemes for hyperbolic conservation laws”, J. Comp. Phys, 49 pp357–393, 1983.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. D.M. Causon, “Numerical computation of external transonic flows”, in Proc. of the 7th Gamm Conf. on Num. Meth. in Fl. Mech., Vieweg 1988.

    Google Scholar 

  3. P.K. Sweby, “High resolution schemes using flux limiters for hyperbolic conservation laws”, Siarn J. Num. Anal. 21 No 5 pp995–1011, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  4. Lax P. and Wendroff B., “Systems of conservation laws”, Comm. on Pure and App. Math., 13 pp217–237, 1960.

    Article  MathSciNet  MATH  Google Scholar 

  5. Davis S.F. “T.V.D. finite difference schemes and artificial viscosity”, ICASE report

    Google Scholar 

  6. Harten A., “The artificial compression method for computation of shocks and contact discontinuities: m. Self-adjusting hybrid schemes”, Math. of Comp. 32 No 142, pp363–389, 1978.

    MathSciNet  MATH  Google Scholar 

  7. Lax P. “Shock waves and entropy”, Proc. Symp at the Univ. of Wisconsin. E.H. Zarantonello, 110, ed. pp603-634, 1971.

    Google Scholar 

  8. Merriam M.L. “Smoothing and the second law”, Comp. Meth. in App. Mech. and Eng. 64 pp177–193, 1987.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Roe P.L. “Approximate Riemann solvers, parameter vectors and difference schemes”, J. Comp. Phys., 43 pp357–372, 1981.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Roe P.L and Pike J., “Efficient construction and utilisation of approximate Riemann solutions”, Comp Meth. in App. Sc. and Eng. 6. Ed. R. Glowinski and J.L. Lions. pp.499-518, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Pieter Wesseling

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer Fachmedien Wiesbaden

About this paper

Cite this paper

Clarke, N., Saunders, R., Causon, D.M. (1990). A Convenient Entropy Satisfying T.V.D. Scheme for Computational Aerodynamics. In: Wesseling, P. (eds) Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 29. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13975-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-663-13975-1_7

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-07629-0

  • Online ISBN: 978-3-663-13975-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics