Multidimensional Flux-Vector-Splitting and High-Resolution Characteristic Schemes

  • Sebastian Noelle


Since the work of Godunov, Van Leer, Harten-Lax and Roe, the numerical solution of systems of hyperbolic conservation laws is dominated by Riemann-solver based schemes. These one-dimensional schemes are usually extended to several space-dimensions either by using dimensional-splitting on cartesian grids or by the finite-volume approach on unstructured grids. The first systematic criticism of using one-dimensional Riemann-solvers for multi-dimensional gas-dynamics goes back to Roe himself: the Riemann-solver is applied in the grid- rather than the flow-direction, which may lead to a misinterpretation of the local wave-structure of the solution.


Cartesian Grid Sonic Point Characteristic Scheme Linear Advection Equation Flux Vector Splitting 
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. Billet S and Toro E (1997). On WAF-type schemes for multidimensional hyperbolic conservation laws.J. Comput. Phys. 130, pp 1-24.MathSciNetCrossRefGoogle Scholar
  2. Colella P (1990). Multidimensional upwind methods for hyperbolic conservation laws. J. Comput Phys., 87, pp 171-200.MathSciNetMATHCrossRefGoogle Scholar
  3. Deconinck H, Paillère H Struijs R and Roe P (1993). Multidimensional upwind schemes based on fluctuation-splitting for systems of conservation laws. Comput. Mech.,11, pp 323-340.MATHCrossRefGoogle Scholar
  4. Fey M (1998). Multidimensional upwinding. I. The method of transport for solving the Euler equations. J. Comput. Phys. 143, pp 159-180.MathSciNetMATHGoogle Scholar
  5. Fey M (1998). Multidimensional upwinding. II. Decomposition of the Euler equations into advection equations. J. Comput. Phys. 143, pp 181-199.MathSciNetMATHGoogle Scholar
  6. Fey M, Jeltsch R, Maurer J and Morel AT (1997). The method of transport for nonlinear systems of hyperbolic conservation laws in several space dimensions. Research Report No.97-12, Seminar for Applied Mathematics, ETH Zürich. Google Scholar
  7. LeVeque RJ (1997). Wave Propagation Algorithms for Multidimensional Hyperbolic Systems. J. Comput. Phys. 131, pp 327-353.CrossRefGoogle Scholar
  8. Lukacova-Medvidova M, Morton K and Warnecke G (1997). Evolution Galerkin methods for hyperbolic systems in two space dimensions. Report 97-44, Univ. Magdeburg, GermanyTo appear inMath. Comp., 2000. Google Scholar
  9. Morel AT (1997). A genuinely multidimensional high-resolution scheme for the shallow-water equations. Dissertation, ETH Zürich Diss. No. 11959. Google Scholar
  10. Noelle S (1999). The MoT-ICE: a new high-resolution wave-propagation algorithm based on Fey’s Method of Transport. Invited plenary lecture. “Proceedings of the Second International Symposium on Finite Volumes for Complex Applications - Problems and Perspectives”, Duisburg, Germany, p. 95. For details see Preprint no. 1999-028 at Scholar
  11. Steger J and Warming R (1981). Flux vector splitting of the inviscid gas-dynamic equations with applications to finite difference methods. J. Comput. Phys. 40, pp 263-293.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Sebastian Noelle
    • 1
  1. 1.Institute for Applied MathematicsBonn UniversityGermany

Personalised recommendations