Reference problem
=====================


Geometry
---------

The field studied is a horizontal semi-infinite medium. In practice it measures :math:`\mathrm{3m}`.

C

.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

D

B

A

Coordinates of the points (:math:`m`):


.. csv-table::

    ":math:`A` ", "0", "0"," 0", ":math:`C` ", "3", "0.1"
    ":math:`B` ", "3", "0"," 0", ":math:`D` ", "0", "0.1"



Material properties
----------------------

We only give here the properties on which the solution depends, knowing that the command file contains other material data (elasticity modules,...) which ultimately play no role in the solution of the problem at hand.


+----------------------+-------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Liquid water          |Density (                                                                                              |1000                                                                                                                                                                                                                                              |
+                      + :math:`{\mathit{kg.m}}^{\mathrm{-}3}`                                                                 +                                                                                                                                                                                                                                                  +
|                      |)                                                                                                      | 1                                                                                                                                                                                                                                                |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      | Viscosity                                                                                             |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+----------------------+-------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Homogenized parameters|Permeability                                                                                           |:math:`\mathrm{1,625E-5}m\mathrm{/}s`                                                                                                                                                                                                             |
+                      + :math:`K`                                                                                             +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       | 0.3                                                                                                                                                                                                                                              |
+                      + Porosity                                                                                              +                                                                                                                                                                                                                                                  +
|                      | Sorption isothermal                                                                                   | .. image:: images/Object_1.svg                                                                                                                                                                                                                   |
+                      + Relative permeability                                                                                 +    :width: 266                                                                                                                                                                                                                                   +
|                      |                                                                                                       |    :height: 47                                                                                                                                                                                                                                   |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       + .. image:: images/Object_2.svg                                                                                                                                                                                                                   +
|                      |                                                                                                       |    :width: 266                                                                                                                                                                                                                                   |
+                      +                                                                                                       +    :height: 47                                                                                                                                                                                                                                   +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+----------------------+-------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Initial state         |Pressure                                                                                               |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       + .. image:: images/Object_3.svg                                                                                                                                                                                                                   +
|                      |                                                                                                       |    :width: 266                                                                                                                                                                                                                                   |
+                      +                                                                                                       +    :height: 47                                                                                                                                                                                                                                   +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+                      +                                                                                                       +                                                                                                                                                                                                                                                  +
|                      |                                                                                                       |                                                                                                                                                                                                                                                  |
+----------------------+-------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+



Boundary and initial conditions
-----------------------------------

They are expressed on capillary pressure:


.. image:: images/Object_4.svg
    :width: 266
    :height: 47


.. _RefImage_Object_4.svg:


.. image:: images/Object_5.svg
    :width: 266
    :height: 47


.. _RefImage_Object_5.svg:

and

.. image:: images/Object_6.svg
    :width: 266
    :height: 47


.. _RefImage_Object_6.svg:

We are in Richards' condition:

.. image:: images/Object_7.svg
    :width: 266
    :height: 47


.. _RefImage_Object_7.svg: