双重互易边界元法在求解N—S方程中的应用

提出了用双互易边界元法求解Ｎ－Ｓ方程的新思路。用Ｐｅａｃｅｍａｎ－Ｒａｃｈｆｏｒｄ算子分理解将时间相依的Ｎ－Ｓ方程分解为线性和非线性子问题，线性问题用共轭梯度法解除压强－速度的耦合；非线性问题进行局部线化。对所得的Ｐａｓｓｉｏｎ方程及相关类型方程采用双重互易的边界元法求解，消除了传统Ｎ－Ｓ方程边界元解法的区域积分问题。

BEM Dual Reciprocity Method for N S Equation

A new boundary element method (BEM) approach for incompressible unsteady viscous N S equation in primitive variables is presented. The Peaceman Rachford operator splitting method is used to discretize the time dependent Navier Stokes equation into linear and nonlinear subproblems. The variables in the linear subproblem are decoupled by a conjugate gradient method and the nonlinear one is treated as a quasilinear problem. The resultant equations are solved by using the Dual Reciprocity Boundary Element Method. The traditional mesh distortion problem in BEM is avoided.