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

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

摘要: 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。
- 广义Stokes方程 /
- Navier-Stokes方程 /
- 边界元方法
Abstract: 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...
- generalized Stokes equation /
- Navier-Stokes equation /
- boundary element method