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

J. M. Granados, C. A. Bustamante, H. Power, W. F. Florez, C. Nieto

    Research output: Chapter in Book/Report/Conference proceedingConference and proceedingspeer-review

    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.

    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
    Pages681-692
    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 method
    • Particular solutions
    • RBF

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