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docs/source_docs/user_guide/inputs/porous_media_defs.rst
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.. _InputsPorousMediaDefs:
Porous Media definitions
========================
Porous media
============
Homogeneous porous media are modeled by the addition of a momentum
source term, :math:`\boldsymbol{S}_{pm}`, to the fluid momentum equation.
.. math::
\boldsymbol{S}_{pm} =-\frac{\mu_f}{C_1} \boldsymbol{u}_f - C_2\frac{1}{2}\rho_f\lvert \boldsymbol{u}_f \rvert \boldsymbol{u}_f
:math:`\mu_f`, :math:`\rho_f`, and :math:`\boldsymbol{u}_f` are the fluid viscosity, density, and velocity and
:math:`C_1` and :math:`C_2` are user defined constants.
The following inputs are defined using the ``pm`` prefix.
+--------------------------+--------------------------------------------------------------------------+----------+-----------+
| | Description | Type | Default |
+==========================+==========================================================================+==========+===========+
| regions | Regions used to define porous media. | String | None |
+--------------------------+--------------------------------------------------------------------------+----------+-----------+
| [region].fluid.volfrac | Fluid volume fraction of the porous media region. | Real | None |
+--------------------------+--------------------------------------------------------------------------+----------+-----------+
| [region].c1 | Porous media permeabilty constant for the source term in fluid | Real | None |
| | momentum equation. | | |
| | | | |
| | :math:`S_i =-\frac{\mu}{C_1} v_i - C_2\frac{1}{2}\rho\lvert v \rvert v_i`| | |
| | | | |
+--------------------------+--------------------------------------------------------------------------+----------+-----------+
| [region].c2 | Porous media inertial resistance factor for the source term in fluid | Real | None |
| | momentum equation. | | |
| | | | |
| | :math:`S_i =-\frac{\mu}{C_1} v_i - C_2\frac{1}{2}\rho\lvert v \rvert v_i`| | |
| | | | |
+--------------------------+--------------------------------------------------------------------------+----------+-----------+
+--------------------------+------------------------------------------------------------------------------+----------+-----------+
| | Description | Type | Default |
+==========================+==============================================================================+==========+===========+
| regions | Regions used to define porous media. | String | None |
+--------------------------+------------------------------------------------------------------------------+----------+-----------+
| [region].fluid.volfrac | Fluid volume fraction of the porous media region. | Real | None |
+--------------------------+------------------------------------------------------------------------------+----------+-----------+
| [region].c1 | Porous media permeabilty constant for the source term in fluid | Real | None |
| | momentum equation. | | |
+--------------------------+------------------------------------------------------------------------------+----------+-----------+
| [region].c2 | Porous media inertial resistance factor for the source term in fluid | Real | None |
| | momentum equation. | | |
+--------------------------+------------------------------------------------------------------------------+----------+-----------+