A transient model for the ITER cryogenic viscous compressor (CVC) is presented. The CVC is designed to separate hydrogen isotopes from helium in the gasmixture exhaust from the ITER torus. During their residence in the CVC, hydrogen isotopes are captured along the pump wall while helium flows through. The CVC thereby provides the first stage of helium compression. The transient model characterizes the transport phenomena (species, momentum, and energy) that occur in the CVC. The numerical results are compared with experimental data from a scaled down test of the ITER CVC using pure hydrogen. Although the model has been developed for a hydrogen-helium mixture, it is simplified here in order to compare with the experimental data. The transient model, along with other numerical models we have developed, provide guidance for the design and optimization of the ITER CVC. The model can also be a useful tool or a reference for similar analyses, such as those for cryogenic carbon capture and air ingress in vacuum isolated cryogenic vessels.