# Cellular Automata/Fluid Dynamics

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

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.

## References

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