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

Carlos A. Bustamante, Henry Power, Cesar Nieto, Whady F. Florez

    Resultado de la investigación: Capítulo del libro/informe/acta de congresoContribución a la conferenciarevisión exhaustiva

    Resumen

    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.

    Idioma originalInglés
    Título de la publicación alojadaPANACM 2015 - 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015
    EditoresSergio R. Idelsohn, Sergio R. Idelsohn, Victorio Sonzogni, Alvaro Coutinho, Marcela Cruchaga, Adrian Lew, Miguel Cerrolaza
    EditorialInternational Center for Numerical Methods in Engineering
    Páginas775-786
    Número de páginas12
    ISBN (versión digital)9788494392825
    EstadoPublicada - 1 abr. 2015
    Evento1st Pan-American Congress on Computational Mechanics, PANACM 2015 and the 11th Argentine Congress on Computational Mechanics, MECOM 2015 - Buenos Aires, Argentina
    Duración: 27 abr. 201529 abr. 2015

    Serie de la publicación

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

    Conferencia

    Conferencia1st Pan-American Congress on Computational Mechanics, PANACM 2015 and the 11th Argentine Congress on Computational Mechanics, MECOM 2015
    País/TerritorioArgentina
    CiudadBuenos Aires
    Período27/04/1529/04/15

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