不可压N-S方程基于流动条件插值方法研究  

A Flow-condition-based Interpolation Method for Incompressible N-S Equations

作　　者：韩向科[1] 苏波[2] 

机构地区：[1]同济大学土木工程学院,上海200092 [2]江苏大学理学院,镇江212013

出　　处：《力学季刊》2010年第3期401-405,共5页Chinese Quarterly of Mechanics

摘　　要：将一维对流扩散方程的解析解作为N-S方程中对流速度插值函数,可以较为精确地反映该单元内部的流动情况,并且自然地引入了对流项的迎风效应,从而避免了传统处理数值振荡方法中附加的稳定项。同时文中运用分裂算法求解N-S方程组,避免了BB(Babuska-Brezzi)条件对于速度压强插值函数阶数的限制,使得对流项插值函数的构造简单易行。构造了一种基于流动条件插值的平面四边形流体单元,并编制了相应的计算程序。详细给出了基于流动条件插值函数的构造过程,给出了分裂算法的计算步骤和公式,继而通过数值算例验证了所构造单元的有效性和准确性,并验证了算法的正确性。The analytical solution of one-dimensional advection - diffusion equation was adopted as the interpolation function of the advection velocity in Navier Stokes equations. The flow condition of element is presented more exactly, and the up-wind effect can be introduced naturally, thus the additional stability term result from numerical computation is avoided. To avoid Babuska-Brezzi condition and simplify the interpolation of advection term, the split scheme was used to solve Navier Stokes equations. A two dimension four-node bilateral fluid element was constructed and a corresponding program was developed. The solution procedure was discussed in detail and the numerical example solution was given to illustrate the capabilities of the procedure.

关 键 词：插值函数 对流扩散方程 分裂算法 N—S方程 

分 类 号：O357.1[理学—流体力学]