Five spacecraft-plasma models are used to simulate the interaction of a simplified geometry Solar Probe Plus (SPP) satellite with the space environment under representative solar wind conditions near perihelion. By considering similarities and differences between results obtained with different numerical approaches under well defined conditions, the consistency and validity of our models can be assessed. The impact on model predictions of physical effects of importance in the SPP mission is also considered by comparing results obtained with and without these effects. Simulation results are presented and compared with increasing levels of complexity in the physics of interaction between solar environment and the SPP spacecraft. The compariso...