Skip to main content

How Effective Are High-Order Approximations in Shock-Capturing Methods? Is There a Law of Diminishing Returns?

  • Conference paper
Computational Fluid Dynamics 2004

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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.

References

  1. D. Balsara and C.-W. Shu. Monotonicity preserving weighted essentially nonoscillatory schemes with increasingly high order of accuracy. Journal of Computational Physics, 160(2):405–452, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. S. Balsara. Total variation diminishing scheme for adiabatic and isothermal magnetohydrodynamics. Astrophysical J. Supp. Ser., 116:133–153, 1998.

    Article  Google Scholar 

  3. P. Colella. A direct Eulerian MUSCL scheme for gas dynamics. SIAM Journal on Scientific and Statistical Computing, 6:104–117, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Colella and P. Woodward. The piecewise parabolic method (PPM) for gasdynamical simulations. Journal of Computational Physics, 54:174–201, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. W. Cook and W. H. Cabot. A high-wavenumber viscosity for high-resolution numerical methods. Journal of Computational Physics, 195(2):594–601, April 2004.

    Article  MATH  Google Scholar 

  6. J. Greenough and W. J. Rider. A quantitative comparison of numerical methods for the compressible Euler equations. fifth-order WENO and piecewiselinear Godunov. Journal of Computational Physics, 196(1):259–281, 2004. Los Alamos Unlimited Release Report, LA-UR-02-5640.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. T. Huynh. Accurate upwind methods for the Euler equations. SIAM Journal on Numerical Analysis, 32:1565–1619, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. G.-S. Jiang and C.-W. Shu. Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 126:202–228, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Majda and S. Osher. Propogation of error into regions of smoothness for accuracte difference approximations to hyperbolic equations. Communications on Pure and Applied Mathematics, 30:671–705, 1977.

    MATH  MathSciNet  Google Scholar 

  10. W. J. Rider. An adaptive Riemann solver using a two-shock approximation. Computers and Fluids, 28:741–777, 1999.

    Article  MATH  Google Scholar 

  11. W. J. Rider, J. A. Greenough, and J. R. Kamm. Extrema, accuracy and monotonicity preserving methods for compressible flows. Technical Report AIAA-2003-4121, 16th AIAA CFD Conference June 23–26, 2003 Orlando FL, 2003.

    Google Scholar 

  12. W. J. Rider, J. A. Greenough, and J. R. Kamm. Extrema, accuracy and monotonicity preserving methods through adaptive nonlinear hybridizations. jcp, to be submitted, 2004.

    Google Scholar 

  13. C.-W. Shu and S. Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics, 77:439–471, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  14. G. Sod. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. Journal of Computational Physics, 27:1–31, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Suresh and H. T. Huynh. Accurate monotonicity-preserving schemes with Runge-Kutta time stepping. Journal of Computational Physics, 136:83–99, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  16. B. van Leer. Towards the ultimate conservative difference scheme. V. A secondorder sequel to Godunov’s method. Journal of Computational Physics, 32:101–136, 1979.

    Article  Google Scholar 

  17. P. Woodward and P. Colella. The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 54:115–173, 1984.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rider, W.J., Kamm, J.R. (2006). How Effective Are High-Order Approximations in Shock-Capturing Methods? Is There a Law of Diminishing Returns?. In: Groth, C., Zingg, D.W. (eds) Computational Fluid Dynamics 2004. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-31801-1_56

Download citation

  • DOI: https://doi.org/10.1007/3-540-31801-1_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31800-2

  • Online ISBN: 978-3-540-31801-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics