To understand the value, popularity and role of the Boltzmann approach to fluid modelling, it is important to situate it within the spectrum of fluid modelling approaches, sitting as it does flexibly between continuum and discrete approaches. This unique conceptual position allows the Boltzmann approach to have the distinct advantage of staying in touch with both the physical basis of fluid flow, in which flows are visualized as being made of a vast number of individual particles, while

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... ing much of the computational tractability of the continuum approach involving PDE formulations. Occupying this middle ground allows Boltzmann approaches to be both useful for prediction in practical problems and yet existentially satisfying to modellers. It is argued that this dual role is a useful grid from which to assess the historical development of the method.