Central-Upwind Schemes for Two-Layer Shallow Water Equations

Alexander Kurganov, Guergana Petrova

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)1742-1773
Number of pages32
JournalSIAM Journal on Scientific Computing
Volume31
Issue number3
DOIs
StatePublished - Jan 2009
Externally publishedYes

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