The Open Pool Australian Light-water (OPAL) reactor Cold Neutron Source (CNS) is a 20 L liquid deuterium thermosiphon system which has performed consistently but will require replacement in the future. The CNS deuterium exploits neutronic heating to passively drive the thermosiphon loop and is cryogenically cooled by forced convective helium flow via a heat exchanger. In this study, a detailed computational fluid dynamics (CFD) model of the complete thermosiphon system was developed for simulation. Unlike previous studies, the simulation employed a novel polyhedral mesh technique. Results demonstrated that the polyhedral technique reduced simulation computational requirements and convergence time by an order of magnitude while predicting thermosiphon performance to within 1% accuracy when compared with prototype experiments. The simulation model was extrapolated to OPAL operating conditions and confirmed the versatility of the CFD model as an engineering design and preventative maintenance tool. Finally, simulations were performed on a proposed second-generation CNS design that increases the CNS moderator deuterium volume by 5 L, and results confirmed that the geometry maintains the thermosiphon deuterium in the liquid state and satisfies the CNS design criteria.