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

In this test case, we study the hydraulic behavior of a saturated porous medium constituted by a single fluid: water in its liquid phase. In *Code_Aster*, it is an HM model. According to the models, the associated fluid behavior law is either of type LIQU_SATU (models A and C) or of type LIQU_GAZ_ATM (models B and D).


Geometry
---------


.. image:: images/Object_2.svg
    :width: 250
    :height: 242


.. _RefImage_Object_2.svg:

Illustration 1: Geometry

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

:math:`A(\mathrm{-}0.5,\mathrm{-}0.5)`; :math:`C(0.5,0.5)`

:math:`B(0.5,\mathrm{-}0.5)`; :math:`D(\mathrm{-}0.5,0.5)`


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


+------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Liquid water            |Density                                                                                                                                                                     |:math:`{10}^{3}`                                                                                                                                                             |
+                        + :math:`({\mathrm{kg.m}}^{-3})`                                                                                                                                             +                                                                                                                                                                             +
|                        |                                                                                                                                                                            | :math:`0.001` :math:`{K}_{e}=3.77{10}^{-9}`                                                                                                                                 |
+                        + Dynamic viscosity of liquid water :math:`(\mathrm{Pa.s})` 1/Compressibility :math:`({\mathit{Pa}}^{\mathrm{-}1})`                                                          +                                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Solid                   |Drained Young's Modulus                                                                                                                                                     |:math:`225{10}^{6}`                                                                                                                                                          |
+                        + :math:`E(\mathrm{Pa})`                                                                                                                                                     +                                                                                                                                                                             +
|                        |                                                                                                                                                                            | :math:`0`                                                                                                                                                                   |
+                        + Poisson's Ratio                                                                                                                                                            +                                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Initial state           |Porosity                                                                                                                                                                    |:math:`0.4`                                                                                                                                                                  |
+                        +                                                                                                                                                                            +                                                                                                                                                                             +
|                        | Temperature :math:`(K)` Liquid Pressure :math:`(\mathrm{Pa})` Vapor Pressure :math:`(\mathrm{Pa})`                                                                         | :math:`273` :math:`0` :math:`1`                                                                                                                                             |
+                        +                                                                                                                                                                            +                                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Constants               |Ideal gas constant                                                                                                                                                          |:math:`8.32`                                                                                                                                                                 |
+------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Homogenized coefficients|Homogenized density                                                                                                                                                         |:math:`1600`                                                                                                                                                                 |
+                        + :math:`({\mathrm{kg.m}}^{-3})`                                                                                                                                             +                                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+                        + Sorption isothermal Biot coefficient Intrinsic permeability :math:`({m}^{2})`                                                                                              + .. image:: images/Object_12.svg                                                                                                                                             +
|                        |                                                                                                                                                                            |    :width: 250                                                                                                                                                              |
+                        +                                                                                                                                                                            +    :height: 242                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+                        +                                                                                                                                                                            +                                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+                        +                                                                                                                                                                            +                                                                                                                                                                             +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+                        +                                                                                                                                                                            + :math:`1` :math:`{K}_{\text{int}}={10}^{-18}`                                                                                                                               +
|                        |                                                                                                                                                                            |                                                                                                                                                                             |
+------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+


**Table** 1.2-1 **: Material data**

The gravity of water is overlooked.


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

Full item:

     blocked trips :math:`{u}_{x}={u}_{y}={u}_{z}=0`

(this is a purely hydraulic case, the mechanics being blocked).

Upper side:

     water flow: :math:`{Q}_{\mathrm{lq}}=0.005{\mathrm{kg.s}}^{-1}\mathrm{.}{m}^{-2}`

Lower side:

     water flow :math:`{Q}_{\mathrm{lq}}=0`

Side faces:

 Elsewhere: zero flow


Initial conditions
--------------------

The displacement fields and liquid pressure fields are initially zero and the reference temperature is set to :math:`{T}_{0}\mathrm{=}273°K`.