The European Space Agency spacecraft Giotto will encounter comet Halley in March 1986 with a relative velocity of 69 km s-1. The fore section of the surface will be bombarded by neutral molecules which will produce secondary electrons and sputtered ions; a plasma cloud will form around the spacecraft, and its surface will be electrically charged. This paper summarizes the results which have been obtained from a numerical simulation of this phenomenon. It is found that a conductive spacecraft will reach a positive potential of the order of 10 V and that a positive potential barrier will develop in the close vicinity of the emitting surface, provided the flux of sputtered ions is sufficient. The charging time constant is approximately equal to the ion plasma period determined by the large ion density in front of the spacecraft. The electron distribution around the spacecraft is nearly isotropic, but the ion diffusion is limited to the forward direction. Thus a well-defined ion wake forms behind the spacecraft. Some numerical aspects of the simulations are also discussed. In particular, it is found that the simulation of spacecraft charging by impact-generated plasmas with the real ion masses is not prohibitively expensive using modern computers.