@inproceedings{8be106e6e7274e8a9f9a9b3362cd6b1f,

title = "Global method of approximate particular solutions for solving the rectangular two-sided lid-driven cavity problem for two-dimensional and incompressible flow",

abstract = "The two-dimensional Navier-Stokes equations in primitive formulation are solved by the global Method of Approximated Particular Solutions (MAPS). The proposed scheme provides a good treatment of the nonlinearities in the momentum equations by using the Newton-Raphson method with variable step. Radial Basis Functions (RBFs) are used as source terms in the Stokes equations in order to obtain particular solutions for the linear part of the momentum equations. A closed-form expression of the particular solutions as a function of domain coordinates are obtained by employing Oseen's decomposition formula. A variation of the classical lid-driven cavity problem, the rectangular two-sided lid-driven cavity flow, is solved with the numerical scheme developed. In this case, the movement of fluid occurs as a result of the constant movement of the two vertical sides. The flow pattern is related to the cavity aspect ratio and the Reynolds number, Re. In this paper, a rectangular cavity with constant height equal to 1 and Re = 700 are considered and the variation in cavity width, 1 ≤ l ≤ 2.5, is analysed. Numerical results reproduce the flow pattern change when increasing l = 1.995 to l = 2 showing good agreement with results reported in the literature.",

keywords = "Meshless method, Particular solutions, RBF",

author = "Granados, {J. M.} and Bustamante, {C. A.} and H. Power and Florez, {W. F.} and C. Nieto",

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 = "681--692",

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",

}