# Porous Media

A *Porous medium* can be defined to specify porousity characteristics of the computational domain.

To model a porous mediuam, navigate to **Advanced Concepts** and under **Porous Media** add a new porous medium. The following models are supported:

## Darcy-Forchheimer

This porousity model takes non-linear effects into account by adding inertial terms to the pressure-flux equation. The model requires both Darcy *d* and Forchheimer *f* coefficients to be supplied by the user. The model leads to the following source term:

$$\vec{S} = – (\mu d + \frac{\rho |\vec{U}|}{2} f) \vec{U}$$

where *μ* represents dynamic viscosity, *ρ* density, and \(\vec{U}\) velocity.

The Darcy *d* coefficient is the reciprocal of the permeability *κ*.

$$d = \frac{1}{\kappa}$$

If the coefficient *f* is set to zero, the equation degenerates into the Darcy equation.

## Fixed coefficients

This model requires *α* and *β* to be supplied by the user. The corresponding source term is:

$$\vec{S} = – \rho_{ref} (\alpha + \beta |\vec{U}|) \vec{U}$$

Additionally, a coordinate system specifies the main directions of the porous zone resistance. The vectors \(\vec{e_1}\) and \(\vec{e_3}\) are unit vectors. The vector \(\vec{e_2}\) is implicitly defined such that \((\vec{e_1} \vec{e_2} \vec{e_3})\) is a right-handed coordinate system like (*x**y**z*). The *x*, *y* and *z* components for *d* and *f* correspond to the vectors \(\vec{e_1}\), \(\vec{e_2}\) and \(\vec{e_3}\) respectively. It can be used to define non-isotropic porosity. For isotropic media, all 3 values should be identical.

Once the setup is complete, a porous region must be assinged. Such a region can be defined using Geometry Primitives.