定常Stokes问题的边界积分方程法

1.前言 定常Stokes问题本身虽然只反映在小雷诺数情况下不可压缩粘性流体的定常流动,然而却为处理完整的Navier-Stokes方程奠定了基础. Stokes问题一般有两种公式化途径,一是通过流函数,二是利用速度-压力公式.两种公式化途径的区域类型数值方法,如有限差分法及有限单元法,已有不少工作,见3]和11].近年来,对这两种公式化途径的边界类型数值方法的研究,也获得一些结果.

A BOUNDARY INTEGRAL EQUATION METHOD FOR SOLVING STATIONARY STOKES PROBLEM

This paper presents an indirect Boundary Integral Equation Method via "velocity-pressure" formulation. The solution of the problem under consideration can be ex-pressed in terms of simple layer potentials, and this expression,which is suitable to theinterior as well as the exterior boundary value problem, leads to a set of boundary in-tegral equations of the first kind. An equivalent variational problem with constraintcan be established. We introduce a Lagrange multiplier to replace the constraint andapply a finite element approach to solve another equivalent variational form. The nu-merical experiments proved the effectiveness of the present method.