Skip to main content

Advertisement

SpringerLink
Log in

Steady-State Computations Using Summation-by-Parts Operators

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

Abstract

This paper concerns energy stability on curvilinear grids and its impact on steady-state calulations. We have done computations for the Euler equations using fifth order summation-by-parts block and diagonal norm schemes. By imposing the boundary conditions weakly we obtain a fifth order energy-stable scheme. The calculations indicate the significance of energy stability in order to obtain convergence to steady state. Furthermore, the difference operators are improved such that faster convergence to steady state are obtained.

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. Mattsson K., Svärd M., Nordström J., Carpenter M.H., (2003). Accuracy Requirements for Transient Aerodynamics. AIAA paper 2003–3689

  2. D.W. Zingg (2000) ArticleTitleComparison of high-accuracy finite-difference methods for linear wave propagation SIAM J. Sci. Comput. 22 476–502 Occurrence Handle10.1137/S1064827599350320

    Article  Google Scholar 

  3. D.W. Zingg S. De Rango M. Memec T.H. Pulliam (2000) ArticleTitleComparison of Several Spatial Discretizations for the Navier-Stokes equations J. Comput. Phys. 160 683–704 Occurrence Handle10.1006/jcph.2000.6482

    Article  Google Scholar 

  4. H.-O. Kreiss G. Scherer (1974) Finite element and finite difference methods for hyperbolic partial differential equations. Mathematical Aspects of Finite Elements in Partial Differential Equations Academic Press Inc New York

    Google Scholar 

  5. Kreiss H.-O., Scherer G. (1977). On the existence of energy estimates for difference approximations for hyperbolic systems Technical report, Dept. of Scientific Computing Uppsala University.

  6. M. Svärd (2004) ArticleTitleOn coordinate transformations for summation-by-parts operators J. Sci. Comput. 20 IssueID1 29–42 Occurrence Handle10.1023/A:1025881528802

    Article  Google Scholar 

  7. K. Mattsson M. Svärd J. Nordström (2004) ArticleTitleStable and Accurate Artificial Dissipation J. Sci. Comput. 21 IssueID1 57–79 Occurrence Handle10.1023/B:JOMP.0000027955.75872.3f Occurrence HandleMR2064326

    Article  MathSciNet  Google Scholar 

  8. M.H. Carpenter D. Gottlieb S. Abarbanel (1994) The stability of numerical boundary treatments for compact high-order finite-difference schemes. 108 IssueID2 272–295

    Google Scholar 

  9. M.H. Carpenter J. Nordström D. Gottlieb (1999) ArticleTitleA Stable and Conservative interface treatment of Arbitrary Spatial Accuracy J. Comput. Phys. 148 341–365 Occurrence Handle10.1006/jcph.1998.6114

    Article  Google Scholar 

  10. J. Nordström M.H. Carpenter (1999) ArticleTitleBoundary and interface conditions for high order finite difference methods applied to the Euler and Navier–Stokes equations J. Comput. Phys. 148 621–645 Occurrence Handle10.1006/jcph.1998.6133

    Article  Google Scholar 

  11. J. Nordström M.H. Carpenter (2001) ArticleTitleHigh-order finite difference methods multidimensional linear problems and curvilinear coordinates J. Comput. Phys. 173 149–174 Occurrence Handle10.1006/jcph.2001.6864

    Article  Google Scholar 

  12. B. Strand (1994) ArticleTitleSummation by parts for finite difference approximations for d/dx J. Comput. Phys. 110 46–67 Occurrence Handle10.1006/jcph.1994.1005

    Article  Google Scholar 

  13. Zingg D.W., (1997). Aspect of linear stability amalysis for higher-order finite-difference methods. AIAA paper 1997–1939.

  14. B. Gustafsson H.-O. Kreiss J. Oliger (1995) Time Dependent Problems and Difference Methods Wiley New York

    Google Scholar 

  15. H.M. Jurgens D.W. Zingg (2000) ArticleTitleNumerical solution of the time-domain maxwell equation using high-accuracy finite-difference methods SIAM J. Sci. Comput. 22 1675–1696 Occurrence Handle10.1137/S1064827598334666

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Magnus Svärd

  2. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Ken Mattsson

  3. Division of Systems Technology, Department of Computational Physics, Department of Information Technology, The Swedish Defence Research Agency, Uppsala University, Uppsala, SE-164 90, Stockholm, Sweden

    Jan Nordström

Authors
  1. Magnus Svärd
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ken Mattsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jan Nordström
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Magnus Svärd.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Svärd, M., Mattsson, K. & Nordström, J. Steady-State Computations Using Summation-by-Parts Operators. J Sci Comput 24, 79–95 (2005). https://doi.org/10.1007/s10915-004-4788-2

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-004-4788-2

Keywords

Search

Navigation