Solution of two-dimensional shallow water equations by a localized radial basis function collocation method

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    Abstract

    A localized version of the Radial Basis Function (RBF) collocation method, is employed for solving the two-dimensional ShallowWater Equations (SWEs). The Newton-Raphson method is used to solve the resulting system of non-linear algebraic equations and a first-order implicit scheme is implemented for temporal discretisation. In order to obtain non-smooth functions which describe height and velocity at supercritical regimes, RBFs are used to approximate dependent variable products instead variable values by means of a local formulation in generalized finite difference fashion. Accurate solutions are obtained for sub-and trans-critical regimes in one-dimensional problems whose analytical solution are reported elsewhere. For verifying two-dimensional spatial and temporal discretization, an oscillatory problem with analytical solution are solved to show the capability of the method for accurately solve 2-D problems. In general, excellent results are achieved regarding the fact that no upwinding scheme are employed when solving transcritical regime problems.

    Original languageEnglish
    Title of host publicationPANACM 2015 - 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015
    EditorsSergio R. Idelsohn, Sergio R. Idelsohn, Victorio Sonzogni, Alvaro Coutinho, Marcela Cruchaga, Adrian Lew, Miguel Cerrolaza
    PublisherInternational Center for Numerical Methods in Engineering
    Pages775-786
    Number of pages12
    ISBN (Electronic)9788494392825
    StatePublished - 1 Apr 2015
    Event1st Pan-American Congress on Computational Mechanics, PANACM 2015 and the 11th Argentine Congress on Computational Mechanics, MECOM 2015 - Buenos Aires, Argentina
    Duration: 27 Apr 201529 Apr 2015

    Publication series

    NamePANACM 2015 - 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015

    Conference

    Conference1st Pan-American Congress on Computational Mechanics, PANACM 2015 and the 11th Argentine Congress on Computational Mechanics, MECOM 2015
    Country/TerritoryArgentina
    CityBuenos Aires
    Period27/04/1529/04/15

    Keywords

    • Meshless methods
    • Non-linear PDE system
    • Radial basis functions
    • Shallow water equations

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