Skip to main content
SpringerLink
Log in

Switched numerical Shuman filters for shock calculations

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Summary

When using Shuman's filtering operator in the numerical computation of shock waves, nonlinear instabilities are prevented, but high order accuracy is lost even in smooth regions. In order to preserve second or higher order accuracy in these regions, an automatic switched Shuman filter is constructed. Nonsteady shock calculations in one and two spatial dimensions, demonstrate the usefulness and accuracy of the method, including examples with third and fourth order accurate finite difference schemes.

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. A. C. Vliegenthart, The Shuman filtering operator and the numerical computation of shock waves,J. of Eng. Math., 4 (1970) 341–348.

    Google Scholar 

  2. P. D. Lax and B. Wendroff, Systems of conservation laws,Comm. Pure Appl. Math., 13 (1960) 217–237.

    Google Scholar 

  3. J. Von-Neumann and R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks,J. of Appl. Phys., 21 (1950) 232–237.

    Google Scholar 

  4. R. D. Richtmyer and K. W. Morton,Difference methods for initial value problems. Second edition, Interscience, New York (1967).

    Google Scholar 

  5. S. Abarbanel and G. Zwas, An iterative finite-difference method for hyperbolic systems,Math. Comp., 23 (1969) 549–565.

    Google Scholar 

  6. S. Z. Burstein, Finite-difference calculations for hydrodynamic flows containing discontinuities,J. Comp. Phys., 2 (1967) 198–222.

    Google Scholar 

  7. P. D. Lax, Weak solutions of non-linear hyperbolic equations and their numerical computation,Comm. Pure Appl. Math., 7 (1954) 159–193.

    Google Scholar 

  8. G. Zwas and S. Abarbanel, Third and fourth order accurate schemes for hyperbolic equations of conservation law form,Math. Comp., 25 (1971) 229–239.

    Google Scholar 

  9. M. Goldberg, Ph.D. thesis, Mathematical Sciences, Tel-Aviv University.

  10. S. Z. Burstein and A. A. Mirin, Third order difference methods for hyperbolic equations,J. Comp. Phys., 5 (1970) 547–565.

    Google Scholar 

  11. G. Zwas and S. Abarbanel,Third and fourth order accuracy schemes for two-dimensional hyperbolic equations, To appear.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tel Aviv University, Israel

    A. Harten & G. Zwas

Authors
  1. A. Harten
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Zwas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Harten, A., Zwas, G. Switched numerical Shuman filters for shock calculations. J Eng Math 6, 207–216 (1972). https://doi.org/10.1007/BF01535103

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01535103

Keywords

Search

Navigation