Upwinding sources at interfaces in conservation laws

Th Katsaounis*, B. Perthame, C. Simeoni

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Hyperbolic conservation laws with source terms arise in many applications, especially as a model for geophysical flows because of the gravity, and their numerical approximation leads to specific difficulties. In the context of finite-volume schemes, many authors have proposed to upwind sources at interfaces, the U.S.I. method, while a cell-centered treatment seems more natural. This note gives a general mathematical formalism for such schemes. We define consistency and give a stability condition for the U.S.I. method. We relate the notion of consistency to the "well-balanced" property, but its stability remains open, and we also study second-order approximations, as well as error estimates. The general case of a nonuniform spatial mesh is particularly interesting, motivated by two-dimensional problems set on unstructured grids.

Original languageEnglish (US)
Pages (from-to)309-316
Number of pages8
JournalApplied Mathematics Letters
Issue number3
StatePublished - Mar 2004
Externally publishedYes


  • Conservation laws
  • Error estimates
  • Finite-volume schemes
  • Second-order approximations
  • Upwinding source terms

ASJC Scopus subject areas

  • Applied Mathematics


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