中国物理B ›› 2006, Vol. 15 ›› Issue (10): 2352-2356.doi: 10.1088/1009-1963/15/10/027

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An analysis of the incompressible viscous flows problem by meshless method

熊渊博, 王　浩   

  1. Department of Engineering Mechanics, Hunan University, Changsha 410082, China
  • 收稿日期:2005-11-14 修回日期:2006-03-21 出版日期:2006-10-20 发布日期:2006-10-20
  • 基金资助:
    Projects Supported by the Project Fund of the Hubei Province Key Lab. of Mechanical Transmission & Manufacturing Engineering Wuhan University of Science & Technology (Grant No 2003A16) is gratefully acknowledged.

An analysis of the incompressible viscous flows problem by meshless method

Xiong Yuan-Bo(熊渊博) and Wang Hao(王浩)†   

  1. Department of Engineering Mechanics, Hunan University, Changsha 410082, China
  • Received:2005-11-14 Revised:2006-03-21 Online:2006-10-20 Published:2006-10-20
  • Supported by:
    Projects Supported by the Project Fund of the Hubei Province Key Lab. of Mechanical Transmission & Manufacturing Engineering Wuhan University of Science & Technology (Grant No 2003A16) is gratefully acknowledged.

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摘要： Generally the incompressible viscous flow problem is described by the Navier--Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-by-step computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton--Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.

关键词: incompressible viscous flows, element-free Galerkin method, Navier--Stokes equation, \\hbox{\hskip 1.9cm} weighted residual method

Abstract: Generally the incompressible viscous flow problem is described by the Navier--Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-by-step computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton--Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.

Key words: incompressible viscous flows, element-free Galerkin method, Navier--Stokes equation, weighted residual method

中图分类号:  (Laminar flows in cavities, channels, ducts, and conduits)

  • 47.15.Rq
02.70.Dh (Finite-element and Galerkin methods) 47.10.ad (Navier-Stokes equations)