For the streamline curvature inverse proposition design of a full three-dimensional centrifugal impeller

a new finite difference method is put forward to solve the S2m stream surface velocity gradient equation. In the difference scheme

forward difference is chosen for the relative velocity derivative along the quasi orthogonal curve; that along the streamline direction is decomposed into two items

forward difference is used for first item

backward difference for another

and forward difference for all other parameter derivatives. The scheme solves the difficulty to guarantee the matrix main diagonal elements being dominant in solving velocity field with simple forward difference or backward difference scheme

and has higher stability and convergence. The new finite difference scheme is taken to redesign Krain impeller. The CFD analysis shows that modified impeller efficiency is increased by 0.3%

and compression ratio is heightened 0.2.