Skip to main content

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM,volume 48))

  • 165 Accesses

Abstract

This chapter presents the construction of the approximation of the space derivatives by centered differences. The schemes must be able to treat discontinuities in the flowfield, i.e. shock waves or vortex sheets. Two ways to handle discontinuities are either to track the shock wave explicitly with an additional algorithm, or to capture it implicitly with the scheme.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

References

  1. Lax, P.D., Wendroff, B.: “Systems of Conservation Laws”. Comm. Pure. Math., Vol. 23, 1960, pp. 217–237.

    Article  MathSciNet  Google Scholar 

  2. Engqvist, B., Osher, S.: “One-Sided Difference Approximations for Nonlinear Conservation Laws”. Math. Comp., Vol. 36, 1981, pp. 321–351.

    Article  MathSciNet  Google Scholar 

  3. Gary, J.: “On Certain Finite Difference Schemes for Hyperbolic Systems”. Math. Comp., Vol. 18, 1964, pp. 1–18.

    Article  MATH  MathSciNet  Google Scholar 

  4. Jameson, A., Schmidt, W., Turkel, E.: “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes”. AIAA Paper 81–1259, 1981.

    Google Scholar 

  5. Jameson, A.: “The Evolution of Computational Methods in Aerodynamics”. J. A.pl. Mech., Vol. 50, 1983, pp. 1052–1070.

    Article  MATH  Google Scholar 

  6. Rizzi, A., Eriksson, L.-E.: “Transfinite Mesh Generation and Damped Euler Equations”. AIAA Paper 81–0999, 1981.

    Google Scholar 

  7. MacCormack, R.W., Paullay, A.J.: “The Influence of the Compuational Mesh on Accuracy for Initial Value Problems with Discontinuous or Nonunique Solutions”. Computers & Fluids, Vol. 2, 1974, pp. 339–361.

    Article  MATH  MathSciNet  Google Scholar 

  8. Lomax, H.: “Some Prospects for the Future of Computational Fluid Dynamics”. AIAA J., Vol. 20, 1982, pp. 1033–1043.

    Article  MATH  MathSciNet  Google Scholar 

  9. Pulliam, T.H.: “Artificial Dissipation Models for the Euler Equations”. AIAA-Paper 85–0438, 1985.

    Google Scholar 

  10. Rizzi, A., Eriksson, L.-E.: “Computation of Flow Around Wings Based on the Euler Equations”. J. Fluid Mech., Vol. 148, 1984, pp. 45–71.

    Article  Google Scholar 

  11. Eriksson, L.-E.: “Transfinite Mesh Generation and Computer-Aided Analysis of Mesh Effects”. Ph.D. Dissertation, Dept. Computer Science, Uppsala Univ., Sweden, 1984.

    Google Scholar 

  12. Olsson, P.: “Flow Calculations Using Explicit Methods on a Data Parallel Computer”. Report No. 117/1989, Uppsala Univ., 1989.

    Google Scholar 

  13. Eriksson. L.-E.: “Boundary Conditions for Artificial Dissipation Operators”. FFA TN 1984–53, Stockholm 1984.

    Google Scholar 

  14. Lomax, H., Pulliam, T.H., Jespersen, D.C.: “Eigensystem Analysis Techniques for Finite-Difference Equations”. AIAA-Paper No. 81–1027, 1981.

    Google Scholar 

  15. Eriksson, L.-E., Rizzi, A.: “Computer-Aided Analysis of the Convergence to Steady State of a Discrete Approximation to the Euler Equations”. J. Comp. Phys., Vol. 57, 1985, pp. 50–128.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Eberle, A., Rizzi, A., Hirschel, E.H. (1992). Centered Differencing. In: Numerical Solutions of the Euler Equations for Steady Flow Problems. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06831-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-663-06831-0_5

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-07634-4

  • Online ISBN: 978-3-663-06831-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics