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}"

mpirun

Case option

--case "github:{repo:toolbox,path:examples/modules/poisson/examples/2Dchannel}"

2. Input parameters

Notation	Quantity	Type	Unit
$\kappa_1$	Permeability of $\Omega_1$	scalar	$m^2Pa^{-1}s^{-1}$
$\kappa_2$	Permeability of $\Omega_2$	idem	idem

Notation

Quantity

Type

Unit

$\kappa_1$

Permeability of $\Omega_1$

scalar

$m^2Pa^{-1}s^{-1}$

$\kappa_2$

Permeability of $\Omega_2$

idem

3. Model & toolbox

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

channel

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

GEO file

CFG file

JSON file

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