The Navier-Stokes equations are obeyed when coarse-graining this type of cellular automata, as long as it has hexagonal symmetry. For 10 points each:
[10h] Name this class of cellular automata exemplified by the FHP model, which models the microscopic interactions of real fluids. Momentum conservation is baked into these automata by their collision rules.
ANSWER: lattice gas automata [or lattice gas cellular automata; accept LGAs or LGCAs]
[10e] Varying the allowed collisions in the FHP model, such as allowing 4-particle collisions, gives rise to macroscopic dynamics with different values of this quantity. This quantity decreases with stress in shear-thinning liquids like ketchup.
ANSWER: viscosity [accept dynamic viscosity or kinematic viscosity; accept coefficient of viscosity or viscosity coefficient]
[10m] The lattice gas automata gave rise to lattice methods named for this equation, which are widely used in computational fluid dynamics. This equation gives the time-evolution of the phase-space distribution function.
ANSWER: Boltzmann equation [or Boltzmann transport equation; or collisionless Boltzmann equation; accept Lattice Boltzmann methods]
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