The viscous incompressible turbulent flow in a vane diffuser was analyzed numerically by using penalty finite element method

based on Galerkin variational finite-element method.During discreting the controlled equations in arbitrary curvilinear coordinates

the consistent formulation of penalty pressure matrix was chosen

and conjected with the streamline upwind Petrov-Galerkin weighed residual formulation to modify the weight function.In reference to the experience of the finite difference method

the streamline upwind term only along the flow direction was controlled by the upwinding parameters.This approach ensured the stability the solution of the pressure.Numerical results of the turbulent flow in the vane diffuser were satisfactorily consistent with the experimental measurements and indicated that the spurious pressure was eliminated while the false diffusion of other terms was simultaneously minimized.