Navier—Stokes（NS）方程组差分计算中的物理和网格尺度效应及NS方程组的简化

对于高Re数流动计算，在通常二阶精度NS差分格式和网格数条件下，存在某些粘性项落入修正微分方程截断误差项的问题。这类NS方程组计算实际是计算某种简化NS方程组，而且重复计算误差物理粘性项既浪费机时和内存，误差积累又会对数值解产生不可预测的影响，避免外述缺陷的办法一个提高NS差分格式的精度，另一个是丢掉可能落入截断误差项的物理粘性项，把NS方程组简化为广义NS方程组，广义NS计算避免了误差物理粘性项误差积累对数值解的不可知影响，又可节省内存和机时，对高Re数流体工程计算很有好处。利用广义NS方程组计算超声速绕前向和后向台阶流动的结果表明：广义NS方程组与NS方程组的数值结果很好相符符。

Effects of physical and grid scales in difference computing of the Navier-Stokes(NS) equations and computing generalized NS-equations

Effects of physical and grid scales in difference computing of NS equations are analyzed and emphasis is on coupling of fluid mechanics with numerical analysis. The study shows that in normal conditions of NS difference computing, some viscous terms will drop into the truncated error terms of modified differential equation of NS difference scheme. In this case, NS computation is actually equal to compute a certain simplified NS equations, moreover, computing repeatedly these viscous error terms yield unpredictable influence on numerical solution. In order to avoid above cited shortcoming, one way is to raise accuracy of NS difference scheme and to fine grid and to realized a veritable computation of NS equations. The other way is to reduce reasonably NS equations. For this end we suggest a generalized NS equations derived by neglecting those error viscous terms from NS equations. The generalized NS equations, in which viscous terms retained are only second order shear viscous terms, may save time and storage and avoid unpredictable influence of error accumulations of error viscous terms on numerical solution. As two examples, both generalized NS (GNS) equations and NS equations are used to compute the supersonic flows over both frontward and rearward facing steps. Numerical results of GNS equations agree well with those of NS equations.