A meshless interpolating Galerkin boundary node method for Stokes flows

作者：Li, Xiaolin^*

来源：Engineering Analysis with Boundary Elements, 2015, 51: 112-122.

DOI：10.1016/j.enganabound.2014.10.019

• Meshless method
• Interpolating Galerkin boundary node method
• Interpolating moving least-square
• Stokes problems

Combining an improved interpolating moving least-square (IIMLS) scheme and a variational formulation of boundary integral equations, a symmetric and boundary-only meshless method, which is called the interpolating Galerkin boundary node method (IGBNM), is developed in this paper for 2D and 3D Stokes flow problems. The IIMLS is used to form shape functions with delta function property. So unlike the Galerkin boundary node method (GBNM), the IGBNM is a direct numerical method in which the basic unknown quantity is the real solution of nodal variables. Besides, to obtain uniqueness of unknown boundary functions and to retain symmetry of system matrices, a Lagrange multiplier is introduced and then a variational formulation with side conditions is gained. Consequently, in the IGBNM, boundary conditions can be applied directly and easily, and the resulting system matrices are symmetric. Thus, the IGBNM gives greater computational precision than the GBNM. The numerical formulae are valid for 2D and 3D Stokes flows and also valid for both interior and exterior problems simultaneously. The capability of the IGBNM is illustrated and assessed by some numerical examples.

• 出版日期2015-2
• 单位重庆师范大学