Applications of Computer-Extended Series

由摄动分析发展而来的计算机扩展级数将用于解决某些流动中的一些悖论。这包括：螺旋管内的流动；波纹管中的流动分离；定常和非定常流动的边界层分离；超小项在低雷诺数流动级数展开中的作用；黏弹性流动在内松弛时间临界值处的收敛问题。在每种情况下，都存在令人困惑的差异和矛盾，这些差异和矛盾阻碍了对其结果充满信心的大规模计算的利用。＊

Computer-extended series, developed from perturbation analysis, will be utilized to resolve a number of paradoxes in certain flows. These are as follows: Flow in a coiled pipe; flow separation in a corrugated pipe; boundary layer separation in both steady and unsteady flow; the role of transcendentally small terms in series expansions for flows at low Reynolds number; and viscoelastic flows with convergence problems at critical values of internal relaxation time. In each case, there exist puzzling discrepancies and paradoxes which have prevented the utilization of large scale computations with confidence in their results. *