含开边界二维Stokes问题的Galerkin边界元解法

本文推导了含有开边界的二维有限域上Stokes问题的边界积分方程, 得出基于单层位势的第一类间接边界积分方程.对与之等价的边界变分方程用Galerkin边界元求解以得出单层位势的向量密度. 对于含有开边界端点的边界单元,采用特别的插值函数, 以模拟其固有的奇异性.论文用若干数值算例模拟了含有开边界的有限区域上不可压缩粘性流体的绕流.  

THE BEM FOR SOLVING 2-D STOKES PROBLEM WITH OPEN BOUNDARY

In this paper, we deduce the boundary integral equation of 2-D Stokes problem in a bounded region containing an open boundary, which is an indirect boundary integral equation based on the single layer potential. Then we solve the boundary variational equation corresponding to the first kind integral equation by Galerkin boundary element method to get the vector density of the single layer potential. For boundary elements containing terminal points on the open boundary , we apply a special interpolating function aimed at simulating its intrinsic singularity. In this paper, several numerical tests simulate the viscous incompressible flow around some open boundary.