广义Stokes方程的完全边界积分表示式及其在求解N-S方程中的应用

为了分解N-S方程组各变量相互偶合,本文采用Peaceman-Rachford算子分裂法,将时间相依的N-S方程组分解成不存在上述偶合特性的线性和非线性的子问题。线性子问题具有广义Stokes方程类型。本文采用多重互易法,即采用多阶拉普拉斯算子基本解逐步变换,将其解表示成完全边界积分形式,从而使问题的计算维数降低一维。广义Stokes方程的算例以及二维圆柱在剪切流中的Stokes绕流解,都表明多重互易算法具有高效特点,而且后者与文3]解析解吻合得非常好。

THE COMPLETE BOUNDARY INTEGRAL FORMULATION FOR GENERALIZED STOKES EQUATION AND ITS APPLICATION TO THE SOLUTION OF NAVIER-STOKES EQUATION

In order to decouple the variables in Navier-Stokes equations, the Peace-man-Rachford operator splitting method is used in this paper to discretize the time dependent Navir-Stokes equations into linear and nonlinear subproblems. In these subproblems the coupling tioned above is avoided. The linear subproblems are quite close to the genearlized Stokes equations A multi-reciprocity method is used to obtain the complete boundary integral formulation for the solution of the generalized Stokes equation to reduce the dimensionality of the problem to be solved by one. The numerical examples for generalized Stokes equations and the Stokes flow of cylindrical body in shear flow show that the multi-reciprocity method presented in this paper is effcient and the results are in good agreement with the analytical solution given in reference 3] .