In this paper, numerical simulations are used to study the turbulent wind noise reduction effect of microphone windscreens with varying shapes and flow resistivities. Typical windscreen shapes consisting of circular, elliptical, and rectangular cylinders are investigated. A turbulent environment is generated by placing a solid circular cylinder upstream of the microphone. An immersed-boundary method with a fifth-order weighted essentially non-oscillatory scheme is implemented to enhance the simulation accuracy for high-Reynolds number flow around the solid cylinder as well as at the interface between the open air and the porous material comprising the windscreen. The Navier-Stokes equations for incompressible flow are solved in the open air. For the flow inside the porous material, a modified form of the Zwikker-Kosten equation is solved. The results show that, on average, the circular and horizontal ellipse windscreens have similar overall wind noise reduction performance, while the horizontal ellipse windscreen with medium flow resistivity provides the most effective wind noise reduction among all the considered cases. The vertical ellipse windscreen with high flow resistivity, in particular, increases the wind noise because of increased self-generation of turbulence.