Coronal mass ejections (CMEs) are a dramatic manifestation of solar activity that release vast amounts of plasma into the heliosphere, and have many effects on the interplanetary medium and on planetary atmospheres, and are the major driver of space weather. CMEs occur with the formation and expulsion of large-scale magnetic flux ropes from the solar corona, which are routinely observed in interplanetary space. Simulating and predicting the structure and dynamics of these interplanetary CME magnetic fields are essential to the progress of heliospheric science and space weather prediction. We discuss the simulation of the 13 May 2005 CME event in which we follow the propagation of a flux rope from the solar corona to beyond Earth orbit. In simulating this event, we find that the magnetic flux rope reconnects with the interplanetary magnetic field, to evolve to an open configuration and later reconnects to reform a twisted structure sunward of the original rope. Observations of the 13 May 2005 CME magnetic field near Earth suggest that such a rearrangement of magnetic flux by reconnection may have occurred.