Central Schemes for Balance Laws

  • G. Russo
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


A brief review is given of shock capturing central schemes for the numerical solution of hyperbolic systems of balance laws. It is shown how to construct high order schemes for conservation laws on a staggered mesh, by using Central Weighted Essentially Non-Oscillatory reconstruction, and how to construct second order central schemes for systems with stiff source which are accurate in the stiff limit. The development of higher order schemes for systems with stiff source is also discussed.


Hyperbolic System Central Scheme Stagger Grid WENO Scheme High Order Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    U. Asher, S. Ruuth, and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time dependent Partial Differential Equations, Appl. Numer. Math. 25, 151–167 (1997).CrossRefGoogle Scholar
  2. 2.
    F. Bianco, G. Puppo, G. Russo, High Order Central Schemes for Hyperbolic Systems of Conservation Laws, SIAM J. Sci. Comp. 21, 294–322 (1999).MathSciNetzbMATHGoogle Scholar
  3. 3.
    A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160, 241–282 (2000).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    S. F. Liotta, V. Romano and G. Russo, Central schemes for balance laws of relaxation type, SIAM J. Numer. Anal. 38, 1337–1356 (2000).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    H. Nessyahu, E. Tadmor, Non-oscillatory Central Differencing for Hyperbolic Conservation Laws, J. Comput. Phys. 87, 408–463 (1990).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    D. Levy, G. Puppo, G. Russo, Central WENO Schemes for Hyperbolic Systems of Conservation Laws, M2AN, 33, 547–571 (1999).zbMATHCrossRefGoogle Scholar
  7. 7.
    D. Levy, G. Puppo, G. Russo, Compact central WENO schemes for multidimensional conservation laws, SIAM J. Sci. Comput. 22, 656–672 (2000).MathSciNetzbMATHGoogle Scholar
  8. 8.
    Xu-Dong Liu, S. Osher, Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids, J. Comput. Phys. 142, 304–330 (1998).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    L. Pareschi, Central differencing based numerical schemes for hyperbolic conservation laws with relaxation terms, Preprint (2000).Google Scholar
  10. 10.
    L. Pareschi, G. Puppo, G. Russo, Central Runge Kutta schemes, in preparation.Google Scholar
  11. 11.
    C.-W. Shu, Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics (editor: A. Quarteroni ), Springer, Berlin (1998).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • G. Russo
    • 1
  1. 1.Dipartimento di Matematica ed InformaticaUniversità di CataniaCataniaItaly

Personalised recommendations