@inproceedings{955cfbea2af34dd789a85728c3c9e127,

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

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.",

keywords = "Meshless methods, Non-linear PDE system, Radial basis functions, Shallow water equations",

author = "Bustamante, {Carlos A.} and Henry Power and Cesar Nieto and Florez, {Whady F.}",

year = "2015",

month = apr,

day = "1",

language = "Ingl{\'e}s",

series = "PANACM 2015 - 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015",

publisher = "International Center for Numerical Methods in Engineering",

pages = "775--786",

editor = "Idelsohn, {Sergio R.} and Idelsohn, {Sergio R.} and Victorio Sonzogni and Alvaro Coutinho and Marcela Cruchaga and Adrian Lew and Miguel Cerrolaza",

booktitle = "PANACM 2015 - 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015",

note = "1st Pan-American Congress on Computational Mechanics, PANACM 2015 and the 11th Argentine Congress on Computational Mechanics, MECOM 2015 ; Conference date: 27-04-2015 Through 29-04-2015",

}