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


Geometry
---------

Consider a cube with side :math:`\mathrm{100m}`.

**H**

**G**

Y

**C**

**D**

X

**F**

**E**

Z

**B**

**A**

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


.. csv-table::

    ":math:`A` ", "0", "0", "0", "100"," 100", ":math:`E` ", "0", "0"
    ":math:`B` ", "100", "0", "0", "100", "100", "0", "0" :math:`F`
    ":math:`C` ", "100", "100", "100", "100"," 100", "100", "100", "0" :math:`G`
    ":math:`D` ", "0", "100", "100", "100"," 100", "100", "100", "0" :math:`H`



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

Only the properties on which the solution depends are given here. The command file contains other material data (elasticity modules, thermal conductivity...) that play no role in the solution of the problem being treated.


+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Liquid water            |Density (                                                                                                                                                                                                                                                                     |103                                                                                                                                                                                                                                                                                                                                  |
+                        + :math:`{\mathrm{kg.m}}^{-3}`                                                                                                                                                                                                                                                 +                                                                                                                                                                                                                                                                                                                                     +
|                        |)                                                                                                                                                                                                                                                                             | 4180 0. 0.001                                                                                                                                                                                                                                                                                                                       |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        | Heat at constant pressure (:math:`{\mathrm{J.K}}^{-1}`) coefficient of thermal expansion of liquid (:math:`{K}^{-1}`) Dynamic viscosity of liquid water (:math:`\mathrm{Pa.s}`) Relative permeability to water                                                               | .. image:: images/Object_1.svg                                                                                                                                                                                                                                                                                                      |
+                        +                                                                                                                                                                                                                                                                              +    :width: 61                                                                                                                                                                                                                                                                                                                       +
|                        |                                                                                                                                                                                                                                                                              |    :height: 21                                                                                                                                                                                                                                                                                                                      |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Vapeur                  |Specific heat (                                                                                                                                                                                                                                                               |1900                                                                                                                                                                                                                                                                                                                                 |
+                        + :math:`{\mathrm{J.K}}^{-1}`                                                                                                                                                                                                                                                  +                                                                                                                                                                                                                                                                                                                                     +
|                        |)                                                                                                                                                                                                                                                                             | 2.5E6. 0.018                                                                                                                                                                                                                                                                                                                        |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        | Initial enthalpy (latent heat of vaporization) :math:`J/\mathrm{Kg}` Molar mass (:math:`{\mathrm{kg.mol}}^{-1}`)                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Gaz                     |Specific heat (                                                                                                                                                                                                                                                               |1900                                                                                                                                                                                                                                                                                                                                 |
+                        + :math:`{\mathrm{J.K}}^{-1}`                                                                                                                                                                                                                                                  +                                                                                                                                                                                                                                                                                                                                     +
|                        |)                                                                                                                                                                                                                                                                             | 0.018                                                                                                                                                                                                                                                                                                                               |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        | Molar mass (:math:`{\mathrm{kg.mol}}^{-1}`) Relative gas permeability Gas viscosity (:math:`{\mathrm{kg.m}}^{-1}\mathrm{.}{s}^{-1}`)                                                                                                                                         | .. image:: images/Object_2.svg                                                                                                                                                                                                                                                                                                      |
+                        +                                                                                                                                                                                                                                                                              +    :width: 61                                                                                                                                                                                                                                                                                                                       +
|                        |                                                                                                                                                                                                                                                                              |    :height: 21                                                                                                                                                                                                                                                                                                                      |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              | 1,8E-5                                                                                                                                                                                                                                                                                                                              |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Dissolved air           |Specific heat (                                                                                                                                                                                                                                                               |1900                                                                                                                                                                                                                                                                                                                                 |
+                        + :math:`{\mathrm{J.K}}^{-1}`                                                                                                                                                                                                                                                  +                                                                                                                                                                                                                                                                                                                                     +
|                        |)                                                                                                                                                                                                                                                                             | 50000                                                                                                                                                                                                                                                                                                                               |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        | Henry's constant (:math:`{\mathrm{Pa.m}}^{3}\mathrm{.}{\mathrm{mol}}^{-1}`)                                                                                                                                                                                                  |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Skeleton                |Heat capacity at constant stress (:math:`{\mathrm{J.K}}^{-1}`)                                                                                                                                                                                                                |1050                                                                                                                                                                                                                                                                                                                                 |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Initial state           |Porosity                                                                                                                                                                                                                                                                      |0.3                                                                                                                                                                                                                                                                                                                                  |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        | Temperature (:math:`K`) Gas Pressure (:math:`\mathrm{Pa}`) Gas Pressure () Vapor Pressure (:math:`\mathrm{Pa}`) Initial Liquid Saturation (:math:`\mathrm{Pa}`)                                                                                                              | 300 1E5 3700 0.5                                                                                                                                                                                                                                                                                                                    |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Constants               |Ideal gas constant                                                                                                                                                                                                                                                            |8,315                                                                                                                                                                                                                                                                                                                                |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Homogenized coefficients|Homogenized density (                                                                                                                                                                                                                                                         |2200                                                                                                                                                                                                                                                                                                                                 |
+                        + :math:`{\mathrm{kg.m}}^{-3}`                                                                                                                                                                                                                                                 +                                                                                                                                                                                                                                                                                                                                     +
|                        |)                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              + .. image:: images/Object_3.svg                                                                                                                                                                                                                                                                                                      +
|                        | Sorption isotherm                                                                                                                                                                                                                                                            |    :width: 61                                                                                                                                                                                                                                                                                                                       |
+                        +                                                                                                                                                                                                                                                                              +    :height: 21                                                                                                                                                                                                                                                                                                                      +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              + With                                                                                                                                                                                                                                                                                                                                +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              | .. image:: images/Object_4.svg                                                                                                                                                                                                                                                                                                      |
+                        +                                                                                                                                                                                                                                                                              +    :width: 61                                                                                                                                                                                                                                                                                                                       +
|                        |                                                                                                                                                                                                                                                                              |    :height: 21                                                                                                                                                                                                                                                                                                                      |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              + .. image:: images/Object_5.svg                                                                                                                                                                                                                                                                                                      +
|                        |                                                                                                                                                                                                                                                                              |    :width: 61                                                                                                                                                                                                                                                                                                                       |
+                        +                                                                                                                                                                                                                                                                              +    :height: 21                                                                                                                                                                                                                                                                                                                      +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+                        +                                                                                                                                                                                                                                                                              +                                                                                                                                                                                                                                                                                                                                     +
|                        |                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                     |
+------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+



Boundary conditions and loads
-------------------------------------

On all sides:

Heat flow

.. image:: images/Object_6.svg
    :width: 61
    :height: 21


.. _RefImage_Object_6.svg:

Zero hydraulic flow