A thermodynamic lattice gas model of Poiseuille flow

Plane Poiseuille flow is simulated using a thermodynamic automaton model. This well-understood problem is used to demonstrate the consistency of the physical predictions obtained from this new lattice gas model with established physical theory. The model presented is a nonrelativistic version of a model constructed by other researchers in which the collision and propagation rules could be used to derive the relativistic Boltzmann equation. The present model has great potential for describing hydrodynamic processes since it does not suffer from many of the limitations of models that rely on differential equations. For example, it can be used to model highly nonlinear processes or flow past complicated boundaries as easily as it can be used for the Poiseuille flow problems presented here. In the present paper, the physical foundations for using this model to study hydrodynamic processes are demonstrated by showing the Boltzmann nature of the gas, the construction of thermodynamic boundary conditions and consistency with physical theory when the temperature dependence of viscosity is modeled. The principal objective of this paper is to establish the physical validity of this model by comparison with well-established theoretical results from equilibrium thermodynamics.