Effective understanding of gas flow is important to ensure efficient operation of gas neutralizer systems such as those used at the Joint European Torus (JET), which form part of invaluable heating systems for nuclear fusion experiments. Computational fluid dynamics modelling of the neutral gas flow in the JET neutraliser has been undertaken, motivated by the shortfall in neutralisation efficiency and apparent loss of gas target observed in the JET neutraliser system. This has presented a challenging modelling endeavour due to the interaction of beam, background plasma and rarefied neutral gas. Utilising the continuum flow approximation, the Navier-Stokes and Augmented Burnett equations have been implemented and applied in conjunction with secondorder slip boundary conditions to form a gas solver accurate within the continuum-transition regime. Simulations in the presence of the ionic beam and background neutraliser plasma encountered during tokamak heating operations have been achieved via the development of a coupled beamplasma- gas solver. The gas flow governing equations have been supplemented by a series of source/sink terms for mass/energy that describe the complex web of interactions between the neutraliser constituents. The developed solver has been validated against experimental data, both in the absence and presence of beam. The design of future gas neutraliser systems has also been considered, with variation of several model and geometry parameters in order to better understand the loss of neutralisation efficiency and how future systems might be optimised. The neutraliser design for the forthcoming International Thermonuclear Experimental Reactor (ITER) has also been evaluated.