KAUST Grant NumberKUS-C1-016-04
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AbstractWe 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.
CitationKurganov A, Petrova G (2009) Central-Upwind Schemes for Two-Layer Shallow Water Equations. SIAM Journal on Scientific Computing 31: 1742–1773. Available: http://dx.doi.org/10.1137/080719091.
SponsorsThe work of this author was supported in part by NSF grant DMS-0610430. Department of Mathematics, Texas A & M University, College Station, TX 77843 ( firstname.lastname@example.org). The work of this author was supported in part by NSF grants DMS-0505501 and DMS-0810869 and by award KUS-C1-016-04 made by King Abdullah University of Science and Technology ( KAUST).