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


Presentation
------------

In this test case, we study the hydraulic behavior of an unsaturated porous medium consisting of two fluids: water in its liquid phase and dry air. In *Code_Aster*, this is a HHM model. The associated law of fluid behavior is of type LIQU_GAZ.


Geometry
---------


.. image:: images/Object_1.svg
    :width: 250
    :height: 242


.. _RefImage_Object_1.svg:

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

:math:`A:-\mathrm{0,5}-\mathrm{0,5}\text{}C:\text{}\mathrm{0,5}\mathrm{0,5}`

:math:`B:\text{}\mathrm{0,5}-\mathrm{0,5}\text{}D:-\mathrm{0,5}\mathrm{0,5}`


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


.. csv-table::

    "Fluid (liquid water)", "Density :math:`({\mathrm{kg.m}}^{-3})`
    Compressibility of liquid :math:`(\mathrm{Pa})`
    Dynamic viscosity of liquid water :math:`(\mathrm{Pa.s})`
    Derived from the viscosity of the fluid with respect to temperature", ":math:`{10}^{3}`
    :math:`{10}^{7}`
    :math:`{10}^{-3}`
    :math:`0.`"
    "Gas (dry air)", "Molar mass :math:`({\mathrm{kg.Pa.K}}^{-1})`
    Gas viscosity :math:`(\mathrm{Pa.s})`
    Derivative of the viscosity of gas with respect to temperature", ":math:`1.8\times {10}^{-3}`
    :math:`{10}^{-5}`
    :math:`0.`"
    "Homogenization coefficients", "Coefficient of :math:`\mathrm{Biot}`
    Porosity", ":math:`1.`
    :math:`0.14`"
    "Homogenized coefficients", "Ideal gas constant"
    Homogenized density :math:`({\mathrm{kg.m}}^{-3})`
    Saturation
    Derivative of saturation with respect to pressure
    Next gravity :math:`X`
    Next gravity :math:`Y`
    Next gravity :math:`Z`
    Intrinsic permeability :math:`({m}^{2})`
    Relative permeability to liquid :math:`({m}^{2})`
    Relative gas permeability :math:`({m}^{2})` "," :math:`8.315`
    :math:`1.6\times {10}^{3}`
    :math:`0.5`
    :math:`0.`
    :math:`0.`
    -10 in 2D, 0 in 3D
    -10 in 3D, 0 in 2D
    :math:`{10}^{-18}`
    :math:`1.`
    :math:`1.`"



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


* Full item:


    * trips :math:`{u}_{x}=0.0m,{u}_{y}=0.0m,{u}_{z}=0.0m`.


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

The displacement fields and capillary pressure fields are initially zero, the dry air pressure is equal to atmospheric pressure and the reference temperature is set to :math:`{T}_{0}=273°K`