.. _sphx_glr_api_gallery_fluids_lattice_boltzmann:

Lattice Boltzmann
-----------------

A kinetic route to the Navier-Stokes equations. Instead of discretizing
the equations of fluid motion, the D2Q9 lattice Boltzmann method moves
populations of fictitious particles along nine lattice directions and
relaxes them toward a local equilibrium. The viscosity is set entirely by
the relaxation time, :math:`\nu = c_s^2(\tau - 1/2)`. Here it reproduces
Poiseuille's parabola and sheds a vortex street behind a cylinder.


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    <div class="sphx-glr-thumbcontainer" tooltip="Lattice gas automata (Frisch, Hasslacher and Pomeau, 1986) showed that Boolean particles hopping and colliding on a hexagonal lattice obey the Navier-Stokes equations on large scales. They were noisy, though. The lattice Boltzmann method (McNamara and Zanetti, 1988) replaced the particles with their average populations f_i, one per lattice direction. Qian, d&#x27;Humières and Lallemand (1992) reduced the collisions to a single relaxation toward a local equilibrium, the BGK operator:">

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  :doc:`/api/gallery/fluids/lattice_boltzmann/plot_lattice_boltzmann_bgk`

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      <div class="sphx-glr-thumbnail-title">The lattice Boltzmann method: Navier-Stokes from colliding populations</div>
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.. toctree::
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   /api/gallery/fluids/lattice_boltzmann/plot_lattice_boltzmann_bgk