.. _vc_flow_through_trees:

==================
Flow Through Trees
==================

The flow's velocity and turbulent kinetic energy are damped when the fluid pass through tree arrangements.
Such situations are common on pedestrian comfort studies.
A good benchmark case to test if the solver is capable of representing such tree structures can be found in :footcite:t:`qi2018numerical` and :footcite:t:`kang2020computational`.

.. figure:: /_static/img/solver/validation/cases/flow_over_tree.svg
    :width: 70%
    :align: center

The measurements of flow profile are made for the average velocity and turbulent kinetic energy, which is defined as:

.. math::
    k=\frac{1}{2}\left(\bar{u'^{2}} +\bar{v'^{2}}+\bar{w'^{2}}\right)
    :label: vc_turbulent_kinetic_energy

.. toctree::
   :maxdepth: -1
   :hidden:

   Flow through trees <10.1_flow_through_trees.ipynb>

.. footbibliography::