Skip to main content
SpringerLink
Log in

Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

Artificial dissipation terms for finite difference approximations of linear hyperbolic problems with variable coefficients are determined such that an energy estimate and strict stability is obtained. Both conservative and non-conservative approximations are considered. The dissipation terms are computed such that there is no loss of accuracy

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. Bretz B., Forsberg K., Nordström J. (2000). High Order Finite Difference Approximations of Hyperbolic Problems, FFA TN 2000-09, Stockholm.

  2. Carpenter M.H., Gottlieb D. (1996). Spectral methods on arbitrary grids. J. Comput. Phys. 129:74–86

    Article  MathSciNet  Google Scholar 

  3. Carpenter M.H., Gottlieb D., Abarbanel S. (1994). The stability of numerical boundary treatments for compact high-order finite difference schemes. J. Comput. Phys. 108(2):272–295

    Article  MathSciNet  Google Scholar 

  4. Carpenter M.H, Nordström J., Gottlieb D. (1999). A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148:341–365

    Article  MathSciNet  Google Scholar 

  5. Gottlieb D., Hesthaven J.S. (2001). spectral methods for hyperbolic problems. J. Comput. and Appl. Math. 128:83–131

    Article  MathSciNet  Google Scholar 

  6. Gustavsson B., Kreiss H.-O, Oliger J. (1995). Time Dependent Problems and Difference Methods. John Wiley&Sons, New York

    Google Scholar 

  7. LeVeque R.J. (1990). Numerical Methods for Conservation Laws. Birkhäuser Verlag, Basel, Boston Berlin

    MATH  Google Scholar 

  8. Mattson K., Nordström J. (2004). Finite difference approximations of second derivatives on summation by parts form. J. Comput. Phys. 199:503–540

    Article  MathSciNet  Google Scholar 

  9. Mattson K., Svärd M., Nordström J. (2004). Stable and accurate artificial dissipation. J. Sci. Comput. 21(1): 57–79

    Article  MathSciNet  Google Scholar 

  10. Strand B. (1994). Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 110:47–67

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Swedish Defence Research Agency, Division of Systems Technology, Computational Physics Department; and the Department of Scientific Computing, Information Technology, Uppsala University, Uppsala, Sweden

    Jan Nordström

Authors
  1. Jan Nordström
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan Nordström.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nordström, J. Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation. J Sci Comput 29, 375–404 (2006). https://doi.org/10.1007/s10915-005-9013-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-005-9013-4

Keywords

Search

Navigation