# DarcyForchheimer

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The Darcy Forchheimer model allows us to simply add a porosity zone into our fluid domain without any expense. In order to use the model, you have to put a fvOptions file into the constant folder including the following content (OpenFOAM-v6):

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  dev                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
version     2.0;
format      ascii;
class       dictionary;
location    "constant";
object      fvOptions;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

porosity1
{
type            explicitPorositySource;

explicitPorositySourceCoeffs
{
selectionMode   cellZone;
cellZone        cat1;

type            DarcyForchheimer;

f   (0.63 1e6 1e6);
d   (80.25 1e6 1e6);

coordinateSystem
{
type    cartesian;
origin  (0 0 0);
coordinateRotation
{
type    axesRotation;
e1  (1 0 0);
e2  (0 1 0);
}
}
}
}



# 1 The Darcy-Forchheimer Equation

The Darcy Forchheimer acts in the momentum equation as a sink term $S_m$. Considering the momentum equation, it follows:

$\frac{\partial \rho \textbf{U}}{\partial t} + \nabla (\rho \textbf{U}\textbf{U}) = \nabla \boldsymbol \sigma + S_m$

Here, the Cauchy stress tensor $\boldsymbol \sigma$ is not split into its deviatoric and hydrostatic part (shear-rate and pressure). The main important term is the source term $S_m$ which is given as:

$S_m = -\left(\mu \textbf{D} + \frac{1}{2}\rho\operatorname{tr}(\textbf{U}\bullet\textbf{I})\textbf{F}\right)\textbf{U}$

While the coefficients $\textbf{D}$ and $\textbf{F}$ have to be specified in the fvOptions file (see code above). The souce term $S_m$ represents a sink as the sign is negative.

In Progress...