非定常不可压Navier-Stokes方程的高效和稳健的差分格式Ⅱ  

EFFICIENT AND ROBUST FINITE DIFFERENCE SCHEMES FOR THE UNSTEADY NAVIER-STOKES EQUATIONS Ⅱ

作　　者：黄兰洁[1] 伍亚丹[1] 

机构地区：[1]中国科学院计算数学与科学工程计算研究所

出　　处：《计算数学》1997年第1期58-72,共15页Mathematica Numerica Sinica

基　　金：国家自然科学基金;攀登计划及中国科学院力学所LNM开放研究实验室资助

摘　　要：A second order accurate implicit finite difference scheme CNMT2 is proposed in this paper for the unsteady incompressible Navier-Stokes equations. It is proved that the scheme is unconditionally nonlinearly stable on smoothly nonuniform halfstaggered meshes; this stability also holds for this scheme with the pressure correction projection method. However, it is found that the pressure correction projection method may lead to deviation problems in practical simulation of high Re flow;the reason and the cure is given in this paper in terms of differential-algebraic equations.A second order accurate implicit finite difference scheme CNMT2 is proposed in this paper for the unsteady incompressible Navier-Stokes equations. It is proved that the scheme is unconditionally nonlinearly stable on smoothly nonuniform halfstaggered meshes; this stability also holds for this scheme with the pressure correction projection method. However, it is found that the pressure correction projection method may lead to deviation problems in practical simulation of high Re flow;the reason and the cure is given in this paper in terms of differential-algebraic equations.

关 键 词：N-S方程 不可压缩流 不定常流 差分格式 

分 类 号：O357.1[理学—流体力学] O241.82[理学—力学]