# Porous media¶

A *Porous medium* can be defined to specify porousity characteristics of the computational domain. This chapter shows how a simulation with a porous medium should be set up on the SimScale platform.

## Creation of a porous medium¶

In the tree, navigate to “Advanced Concepts” and under *Porous Media* add a *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 \(\mu\) represents dynamic viscosity, \(\rho\) density, and \(\vec{U}\) velocity.

The Darcy \(d\) coefficient is the reciprocal of the permeability \(\kappa\).

\[d = \frac{1}{\kappa}\]If the coefficient \(f\) is set to zero, the equation degenerates into the Darcy equation.

- Fixed coefficients
This model requires \(\alpha\) and \(beta\) 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.

In this example, the catalytic converter in an exhaust manifold is modeled using a porous medium. The porous region is defined using a cartesian box.