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    Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

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    Type
    Article
    Authors
    Bryson, Steve
    Epshteyn, Yekaterina
    Kurganov, Alexander
    Petrova, Guergana
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2010-10-11
    Online Publication Date
    2010-10-11
    Print Publication Date
    2011-05
    Permanent link to this record
    http://hdl.handle.net/10754/600189
    
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    Abstract
    We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.
    Citation
    Bryson S, Epshteyn Y, Kurganov A, Petrova G (2010) Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system. ESAIM: Mathematical Modelling and Numerical Analysis 45: 423–446. Available: http://dx.doi.org/10.1051/m2an/2010060.
    Sponsors
    The research of Y. Epshteyn is based upon work supported by the Center for Nonlinear Analysis (CNA) under the NSF Grant # DMS-0635983. The research of A. Kurganov was supported in part by the NSF Grant # DMS-0610430. The research of G. Petrova was supported in part by the NSF Grant # DMS-0810869 and Award # KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    EDP Sciences
    Journal
    ESAIM: Mathematical Modelling and Numerical Analysis
    DOI
    10.1051/m2an/2010060
    ae974a485f413a2113503eed53cd6c53
    10.1051/m2an/2010060
    Scopus Count
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