The Toroidal Dust Mobilization eXperiment (TDMX) has been developed to investigate the mobilization of dust in fusion reactor Loss of Vacuum Accident (LOVA) scenarios. TDMX data will be utilized to validate new computational models for dust resuspension and transport in LOVAs. This work describes the modeling of the compressible vessel filling in TDMX using the CFD code Fluent. Results for fast (~0.1 s) pressure transients are found to agree well with experimental and analytical results. Modeling longer transients has thus far been less successful, due primarily to the difficulty in resolving the accompanying small flow passages.