Skip to main content

The GRP Treatment of Flow Singularities

  • Chapter
Computational Fluid Dynamics

Abstract

The GRP (Generalized Riemann Problem) method was introduced and developed in [1–7, 9–10], following the pioneering work of van Leer [13].

Partially supported by the Robert Szold Institute for Applied Science of the P.E.F. Israel Endowment Funds.

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. M. Ben-Artzi: The Generalized Riemann Problem in compressible duct flow, Contemporary Mathematics 60 (1987), 11–18 (Ed. B. Keyfitz)

    Google Scholar 

  2. M. Ben-Artzi: The Generalized Riemann Problem for reactive flows, J. Comp. Phys. 81 (1989), 70–101

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. M. Ben-Artzi, A. Birman: Application of the “Generalized Riemann Problem” method to 1-D compressible flows with material interfaces, J. Comp. Phys. 65 (1986), 170–178

    Article  ADS  MATH  Google Scholar 

  4. M. Ben-Artzi, A. Birman: Computation of reactive duct flows in external fields, J. Comp. Phys. 86 (1990), 225–255

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. M. Ben-Artzi, J. Falcovitz: A second-order Godunov-type scheme for compressible fluid dynamics, J. Comp. Phys. 55 (1984), 1–32

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Ben-Artzi, J. Falcovitz: A high-resolution upwind scheme for quasi 1-D flows, in “Numerical Methods for the Euler Equations of Fluid Dynamics”, Eds. F. Angrand, A. Dervieux, J.A. Desideri, R. Glowinski, SIAM Publ. 1985, pp. 66–83

    Google Scholar 

  7. M. Ben-Artzi, J. Falcovitz: An upwind second-order scheme for compressible duct flows, SIAM J. Sei. Stat. Comp. 7 (1986), 744–768

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Courant, K.O. Friedrichs: Supersonic flow and shock waves, Springer-Verlag, New York 1976

    MATH  Google Scholar 

  9. J. Falcovitz, A. Birman: A singularities tracking conservation laws scheme for compressible duct flows, in “Shock Waves: Proc. of the 18th Int. Symp. on Shock Waves” (Ed. K. Takayama ), Springer-Verlag 1991, pp. 1107–1112

    Google Scholar 

  10. J. Falcovitz, A. Birman: A singularities tracking conservation laws scheme for compressible duct flows, J. Comp. Phys. (in press)

    Google Scholar 

  11. S.K. Godunov: A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sbornik 47 (1959), 271–295

    MathSciNet  Google Scholar 

  12. G.A. Sod: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comp. Phys. 27 (1978), 1–31

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. B. van Leer: Towards the ultimate conservative difference scheme, V, J. Comp. Phys. 32 (1979), 101–136

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ben-Artzi, M., Birman, A., Falcovitz, J. (1995). The GRP Treatment of Flow Singularities. In: Leutloff, D., Srivastava, R.C. (eds) Computational Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79440-7_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-79440-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-79442-1

  • Online ISBN: 978-3-642-79440-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics