求解定常势流正命题的全时-空变分有限元法

非定常流动变分原理的建立使得用有限元法来求解多工况点的设计问题成为可能。本文在刘高联的非定常变分理论的基础上，对定常变分问题进行时间相关有限元求解。但由于可压缩非定常位势流动的控制方程是双曲型的，简单地把时间当作同空间一样的物理维来求解是不可行的。而现有的时-空有限元法极其复杂，增加了计算复杂度，使其很难用于工程设计中。为此，文[2、3]提出了求解一维非定常问题的新型时-空有限元法。本文把该方法推广到二维流动，用它求解二维弯管内的流动和翼型绕流问题。计算结果与用定常方法求得的结果几乎重合，说明该方法可以用于多维时间相关求解。

A New Time/Space FEM for Steady Potential Flow

On the basis of Liu Gaolian's unsteady variational theories, the time-marching method is used to solve steady variational problems. Because the governing equations for compressible unsteady potential flow is hyperbolic, looking time dimension as space dimension in the same way is never appropriate. Unfortunately, the existing time/space FEM is quite complicated, and difficult to be put into engineering use. A new time/space FEM was presented to calculate the one-dimensional unsteady problems in papers [2,3]. The method is now extended to calculate two-dimensional steady flow in a time-marching way. As examples, one pipe flow and one airfoil rounding flow are considered. The results agree well with those of the steady flows, which demonstrates the usefulness of this method in solving multidimensional problems.