Skip to main content
SpringerLink
Log in

On a Class of High Resolution Methods for Solving Hyperbolic Conservation Laws with Source Terms

  • Chapter
Applied Nonlinear Analysis

  • 643 Accesses

Abstract

A class of conservative numerical methods for solving hyperbolic nonhomogeneous scalar conservation laws is presented. Convergence and stability properties are studied. Particular attention is devoted to time depending point sources. Several numerical examples are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
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. Chalabey, A. (1997). On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms. Math. Comp., 66(218):527–545.

    MathSciNet  Google Scholar 

  2. Fletcher, C.A.J. (1998). Computational Techniques for Fluid Dynamics. Vol. II, Spriger-Verlag.

    Google Scholar 

  3. Greenberg, J.M., Leroux, A.Y., Baraille, R. and Noussair, A. (1997). Analysis and approximation of conservative laws with source terms. SIAM J. Numer. Anal., 34(5):1980–2007.

    Article  MathSciNet  Google Scholar 

  4. Koren, B. (1993). A robust upwind discretization method for advection, diffusion and source terms. Notes on Numerical Fluid Mechanics, 45 (Vieweg, Braunschweig, 1993), 117–138.

    Google Scholar 

  5. Lax, P. and Wendroff, B. (1960). Systems of Conservation Laws. Comm. Pure Appl. Math., 13:217–237.

    MathSciNet  Google Scholar 

  6. LeVeque, R.J. (1992) Numerical Methods for Conservation Laws. Birkhauser, Berlin.

    Google Scholar 

  7. LeVeque, R.J. and Yee, H.C. (1990). A study of numerical methods for hyperbolic conservation laws with stiff source terms. J. Comp. Phys., 86:187–210.

    Google Scholar 

  8. Roe, P.L. (1985). Some contributions to the modeling of discontinuous flows. Lectures in Appl. Math., 22:163–193.

    MathSciNet  MATH  Google Scholar 

  9. Santos, J. and de Oliveira, P. A converging finite volume scheme for hyperbolic conservation laws with source terms. J. Comp. Appl. Math. To appear.

    Google Scholar 

  10. Schroll, H.J. and Winther, R. (1996). Finite-difference schemes for scalar conservation laws with source terms. IMA J. Numer. Anal., 16:201–215.

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. Paula de Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. I.S.T. Technical University, Lisbon, Portugal

    Adélia Sequeira  & Juha Hans Videman  & 

  2. University of Pisa, Pisa, Italy

    Hugo Beirão da Veiga

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

de Oliveira, P., Santos, J. (2002). On a Class of High Resolution Methods for Solving Hyperbolic Conservation Laws with Source Terms. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_27

Download citation

  • DOI: https://doi.org/10.1007/0-306-47096-9_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46303-7

  • Online ISBN: 978-0-306-47096-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation