# 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.