不可压粘流N－S方程的边界积分解法

THE BOUNDARY INTEGRAL METHOD FOR INCOMPRESSIBLE VISCOUS NAIER-STOKES EQUATION

对原变量的Ｎ－Ｓ方程进行一阶时间离散，采用共轭梯度法解除压强－速度的耦合．对所得的一系列Ｌａｐｌａｃｅ方程、Ｐｏｓｓｉｏｎ方程和Ｈｅｌｍｈｏｔｚ方程均进行边界积分法求解，首次得到了粘性Ｎ－Ｓ方程的边界积分表示式．圆柱的定常、非定常尾迹计算结果表明了本文方法的有效性．

The first-order time splitting method is used to discretize the Navier-Stokes equations with primitive variables and a conjugate gradient method is used to decouple the variables.The resulted Laplace equations, Possion equations and Helmhotz equations are solved by using Boundary Integral Method and thus a boundary integral formulation for viscous Navier-Stokes equation is established for the first time.The numerical results for the steady and unsteady viscous flow aroulld cylindical body show the method developed in this paper is efficient.