.. _navier_stokes-navier_stokes:

navier_stokes/navier_stokes.py
==============================

**Description**


Navier-Stokes equations for incompressible fluid flow.

Find :math:`\ul{u}`, :math:`p` such that:

.. math::
    \int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u}
    + \int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v}
    - \int_{\Omega} p\ \nabla \cdot \ul{v}
    = 0
    \;, \quad \forall \ul{v} \;,

    \int_{\Omega} q\ \nabla \cdot \ul{u}
    = 0
    \;, \quad \forall q \;.


.. image:: /../gallery/images/navier_stokes-navier_stokes.png


:download:`source code </../examples/navier_stokes/navier_stokes.py>`

.. literalinclude:: /../examples/navier_stokes/navier_stokes.py

