CAJ | 학술논문

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。避免上述缺陷的办法一个是提高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。
대우고Re수류동계산，재통상이계정도NS차분격식화망격수조건하，존재모사점성항락입수정미분방정절단오차항적문제。저류NS방정조계산실제시계산모충간화NS방정조，이차중복계산오차물리점성항기낭비궤시화내존，오차적루우회대수치해산생불가예측적영향。피면상술결함적판법일개시제고NS차분격식적정도，령일개시주도가능락입절단오차항적물리점성항，파NS방정조간화위엄의NS방정조。엄의NS계산피면료오차물리점성항오차적루대수치해적불가지영향，우가절성내존화궤시，대고Re수류체공정계산흔유호처。이용엄의NS방정조계산초성속요전향화후향태계류동적결과표명：엄의NS방정조여NS방정조적수치결과흔호상부。
Effects of physical and grid scales in difference computing of NSequations 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 dropinto the truncated error terms of modified differential equation of NS differen ce 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 eq uations 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 exa mples, both generalized NS (GNS) equations and NS equations are used to compute the supersonic flows over both frontward and rearward facing steps. Numerical re sults of GNS equations agree well with those of NS equations.