The wake formation behind objects in flowing plasmas is studied for supersonic flow velocities by numerical simulations. The objects are charged self-consistently by plasma currents. The wake structures and Mach cones are studied for various system conditions in the context of wake interactions with other objects, such as dust grains. Additional photoemission currents can lead to a positive charge on the object and significantly modify the wake. The analysis is carried out in two and three dimensions with particle-in-cell numerical codes.