Schwarz alternating domain decomposition approach for the solution of two-dimensional Navier-Stokes flow problems by the method of approximate particular solutions

Carlos Andres Bustamante, Henry Power, Whady Felipe Florez

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    6 Scopus citations

    Abstract

    The method of approximate particular solutions (MAPS) is used to solve the two-dimensional Navier-Stokes equations. This method uses particular solutions of a nonhomogeneous Stokes problem, with the multiquadric radial basis function as a nonhomogeneous term, to approximate the velocity and pressure fields. The continuity equation is not explicitly imposed since the used particular solutions are mass conservative. To improve the computational efficiency of the global MAPS, the domain is split into overlapped subdomains where the Schwarz Alternating Algorithm is employed using velocity or traction values from neighboring subdomains as boundary conditions. When imposing only velocity boundary conditions, an extra step is required to find a reference value for the pressure at each subdomain to guarantee continuity of pressure across subdomains. The Stokes lid-driven cavity flow problem is solved to assess the performance of the Schwarz algorithm in comparison to a finite-difference-type localized MAPS. The Kovasznay flow problem is used to validate the proposed numerical scheme. Despite the use of relative coarse nodal distributions, numerical results show excellent agreement with respect to results reported in literature when solving the lid-driven cavity (up to Re = 10,000) and the backward facing step (at Re = 800) problems.

    Original languageEnglish
    Pages (from-to)777-797
    Number of pages21
    JournalNumerical Methods for Partial Differential Equations
    Volume31
    Issue number3
    DOIs
    StatePublished - 1 May 2015

    Bibliographical note

    Publisher Copyright:
    © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 777-797, 2015.

    Keywords

    • meshless methods
    • Navier-Stokes
    • particular solutions

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