Abstract: Based on the stream function-vorticity expression a discrete procedure is employed to approximate the imcompressible fluid with zero viscosity,in which the vorticity is approximated by finite difference along its streamline,the velocity field and the stream function are approximated simultaneously by a mixed finite element.The analysis shows that the procedure possesses both high accuracy and good stability which are not shared by standard methods.

Key words: imcompressible fluid with zero viscosity, streamline, mixed finite element, numerical simulation