Cellular Automata/Fluid Dynamics

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The basic idea of simulating fluid dynamics with cellular automata is implementing particle dynamics as cellular automata rules and fluid dynamics would emerge as mean properties of

Differential equation model for incompressible fluids[edit]

We are interested in the flow velocity u that is defined by two differential equations

Navier-Stokes equation
 \frac{\partial u}{\partial t} + (u \nabla) u = - \nabla P + \nu \nabla^2 u
continuity equation
 \nabla\cdot u = 0

P=p/\rho_0 is the kinematic pressure, p is the pressure, \rho_0 constant mass density and \nu is the kinematic share viscosity.


  1. Dieter A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models An Introduction, Springer 2000