Darcy flow through a channel

This example can be found from [CL07].

1. Running the case

The command line to run this case is :

mpirun -np 4 feelpp_toolbox_mixed-poisson-model --case "github:{repo:toolbox,path:examples/modules/poisson/examples/2Dchannel}"

2. Input parameters

Notation Quantity Type Unit


Permeability of \(\Omega_1\)




Permeability of \(\Omega_2\)



3. Model & toolbox

We consider a \(100\times100\) square channeled with two poorly porous panes.


The top and bottom boundaries \(\Gamma_{wall}\) are labelled wall, the left inlet \(\Gamma_{left}\) is left and the right outlet \(\Gamma_{right}\) is right. The main porous domain is omega1 while the panes are labeled omega2. The interface is labeled interface.

This example runs within the mixed-poisson toolbox.

4. Boundary conditions

We impose a Neumann no-flow condition on the wall and Dirichlet conditions on the inlet and outlet :

\[\left\{\begin{array}{ll} p=1&\text{on }\Gamma_{left}\\ p=0&\text{on }\Gamma_{right}\\ \underline u\cdot\underline n=0&\text{on }\Gamma_{wall} \end{array}\right.\]

5. Configuration & geometry

6. Output

7. Reference

[CL07] M. R. Correa, A. F. D. Loula, Stabilized velocity post-processings for Darcy flow in heterogeneous porous media, Commun. Numer. Meth. Engng 2007; 23:461–489