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Development of a meshless Galerkin boundary node method for viscous fluid flows

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  • Li, Xiaolin

Abstract

In this paper, a meshless Galerkin boundary node method is developed for boundary-only analysis of the interior and exterior incompressible viscous fluid flows, governed by the Stokes equations, in biharmonic stream function formulation. This method combines scattered points and boundary integral equations. Some of the novel features of this meshless scheme are boundary conditions can be enforced directly and easily despite the meshless shape functions lack the delta function property, and system matrices are symmetric and positive definite. The error analysis and convergence study of both velocity and pressure are presented in Sobolev spaces. The performance of this approach is illustrated and assessed through some numerical examples.

Suggested Citation

  • Li, Xiaolin, 2011. "Development of a meshless Galerkin boundary node method for viscous fluid flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 258-280.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:2:p:258-280
    DOI: 10.1016/j.matcom.2011.07.004
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    References listed on IDEAS

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    1. Lobovský, Libor & Vimmr, Jan, 2007. "Smoothed particle hydrodynamics and finite volume modelling of incompressible fluid flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 124-131.
    2. Mošová, Vratislava, 2007. "Meshless RKHPU method and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 161-165.
    3. Nguyen, Vinh Phu & Rabczuk, Timon & Bordas, Stéphane & Duflot, Marc, 2008. "Meshless methods: A review and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 763-813.
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    Cited by:

    1. Li, Xiaolin & Chen, Hao & Wang, Yan, 2015. "Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 56-78.
    2. Qu, Wenzhen & Chen, Wen & Fu, Zhuojia & Gu, Yan, 2018. "Fast multipole singular boundary method for Stokes flow problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 57-69.

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