.. _bc_free_surface:

============
Free Surface
============

Free surface BCs are frequently adopted at top boundary of a atmospheric flow. They can be implemented from a Neumann BC that considers zero gradient of macroscopic properties.

-------
Neumann
-------

The implemented Neumann BC is used to represent a free surface by forcing a zero normal derivative of macroscopics at the boundary:

.. math::
    \frac{\partial A}{\partial x_{n}}=0;

Where :math:`A` represents any macroscopic variable (:math:`\rho`, :math:`u_{\alpha}`, :math:`S_{\alpha\beta}`). To implement that, the boundary nodes replicate the macroscopic values from the first node towards normal direction.