应用多块分区搭接网格技术和变域变分有限元法设计分流叶栅

该文针对含分流叶片的亚声速平面叶栅的反命题，运用多块分区搭接网格技术将流动区域分成两部分生成计算网格，再根据泛函的驻值必要条件，应用变域变分有限元方法对分流叶栅叶型进行了反设计。变域变分通过把可变边界结合在变分泛函中，使其与求解流场的控制方程结合起来，从而使可变边界求解和流场分析可以完全耦合地进行，因而适合于分流叶栅的反问题研究。由于分流叶片的存在，使得很难在流动区域内生成一体化网格，因此该文应用了多块分区搭接网格技术。该技术可保证每一子域都具有高质量的计算网格，并且子域与子域间的流场信息交换也简单易行。两个典型算例表明了该方法的正确性和优越性。

Multi-block Patched Grid Generation and Variable-Domain Variational Finite Element Method for Shape Design of Splitter Cascades

A splitter blade of 2-D subsonic cascades is designed. First the multi-block patched grid generation technique is used to divide the field into two parts. The variable-domain variational FEM for shape design of cascades is then introduced based on the stationary condition of functionals. By variable-domain variational calculus, the free boundary condition is incorporated into the functionals of variational principles, which makes it possible to calculate both the flow field and the unknown boundary (airfoil shape) simultaneously. It is therefore suitable for the research of splitter cascades' inverse problem. The existence of splitter blade makes it difficult to generate a single grid in the entire flow field. For this reason, the multi-block patched grid generation technique is used. This technique can ensure that the grid is of high quantity in every subdomains and the commutation of flow information between subdomains is simple. Two numerical examples are given to validate the present method.