Skip to main content

An implicit centered scheme which gives non-oscillatory steady shocks

  • Numerical Analysis
  • Conference paper
  • First Online:
Nonlinear Hyperbolic Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1270))

Abstract

We consider the calculation of steady weak solutions of an hyperbolic system in one-space dimension. By using an implicit centered scheme of second-order accuracy with an appropriate treatment of the boundary conditions, we obtain a quick convergence to a non-oscillatory steady solution.

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 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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. LERAT A.-Une classe de schémas aux différences implicites pour les systèmes hyperboliques de lois de conservation, Comptes Rendus Acad. Sc. Paris, Vol. 288A, pp. 1033–1036, 1979.

    MathSciNet  MATH  Google Scholar 

  2. LERAT A., SIDES J. and DARU V.-An Implicit Finite-Volume Method for Solving the Euler Equations, Lecture Notes in Physics, Vol. 170, pp. 343–349, 1982.

    Article  Google Scholar 

  3. LERAT A., Implicit Methods of Second-Order Accuracy for the Euler Equations, AIAA J., Vol. 23, pp. 33–40, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  4. LAX P.D. and WENDROFF B.-Systems of Conservation Laws, Comm. Pure Appl. Math., Vol. 13, pp. 217–237, 1960.

    Article  MathSciNet  MATH  Google Scholar 

  5. DARU V. and LERAT A.-Analysis of an Implicit Euler Solver, in Numerical Methods for the Euler Equations of Fluid Dynamics, F. Angrand and al. Ed, SIAM Publ., pp. 246–280, 1985.

    Google Scholar 

  6. SHUBIN G.R., STEPHENS A.B. and GLAZ H.M.-Steady Shock Tracking and Newton's Method Applied to One-Dimensional Duct Flow, J. Comput. Phys., Vol. 39, pp. 364–374, 1981.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Claude Carasso Denis Serre Pierre-Arnaud Raviart

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Daru, V., Lerat, A. (1987). An implicit centered scheme which gives non-oscillatory steady shocks. In: Carasso, C., Serre, D., Raviart, PA. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078321

Download citation

  • DOI: https://doi.org/10.1007/BFb0078321

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18200-9

  • Online ISBN: 978-3-540-47805-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics