Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics

The semi-inverse method suggested by the author is one of the best and most convenient ways to deduce generalized variational principles with multi-variables from 1) partial differential equations (PDE) and boundary conditions (BC), or 2) known variational principles with single variable or double variables, or 3) a suitable energy trial-functional, without any crisis variational phenomenon. As a result two families of generalized variational principles for irrotational compressible blade-to-blade flow have been deduced without using the Lagrange multiplier method. The method will have a great effect not only in fluid mechanics, but also in elasticity theorems.