Navier-Stokes方程积分表达式的有限元解法

本文采用定常不可压Navier-Stokes（NS）方程的积分表达式方法计算粘性流动问题,用线性三角形单元划分计算区域,建立了适当的迭代求解过程。本文改进了压力计算方法,用全变量松驰加快了收敛速度,用矩阵分块计算减小了内存限制,并可以通过对矩阵特性的分析更好地控制迭代过程的稳定性。

A FINITE ELEMENT METHOD FOR INTEGRAL REPRESENTATIONS OFINAVIER-STOKES EQUATION

The integral representation of the steady, incompressible Navier-Stokes equations have been used for the numerical computations of viscous flows and a finit element solution procedure has been set up.The oscillation problem on the computed pressure function has been resolved by a new pressure evaluation algorithm; the relaxation of all the variables and suitable initial field selection have lead to a great reduction of the iteration steps and so the CPU time; the condition tnumber of the coefficient matrix is calculated and used to determine the proper - under-relaxation factor prior the iteration; and, another improvement results in the elimination of the storage limit. Some of the computational results for Reynolds number from 5 to 104 are given. The computations show that the present method is applicable to efficiently and accurately solve the viscous flow problems with arbitrary boundaries.