Modeling A
==============


Characteristics of modeling
-----------------------------------

Mensi's law of diffusion is used.


Characteristics of the mesh
----------------------------


.. code-block:: text

    The test piece is meshed using 80 QUAD4 evenly distributed. There is only one element in the height.

Number of knots: 162

Number of meshes and type: 80 QUAD4


Characteristics of time discretization
------------------------------------------------


.. csv-table::

    "**Initial Instant (** :math:`s` **)**) **", "**Instant Final (**:math:`s`**) **", "**Number of time steps**"
    "0", "3600", "10"
    "3600", "259 200", "10"
    "259 200", "2 419 200", "10"
    "2 419 200", "39 420 000", "10"
    "39,420,000", "94,608,000", "10"
    "94 608 000", "1 57 680 000", "10"



Tested sizes and results
------------------------------

Water concentration at point :math:`x\mathrm{=}0.0`:


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", ":math:`\text{\%}` **difference**"
    "after 1 hour", "128.80", "128.80", "2.21 10-14"
    "after 3 days", "128.80", "128.80", "-2.21 10-14"
    "after 28 days", "128.80", "128.80", "-3.67 10-5"
    "after 1.25 years", "117.49", "117.49", "117.76", "0.231"
    "after 3 years", "105.06", "105.38", "0.307"
    "after 5 years", "96.77", "97.09", "0.332"


Water concentration at point :math:`x\mathrm{=}0.04`:


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", ":math:`\text{\%}` **difference**"
    "after 1 hour", "128.80", "128.80", "1.31 10-13"
    "after 3 days", "128.80", "128.80", "-1.77 10-13"
    "after 28 days", "128.61", "128.66", "0.038"
    "after 1.25 years", "117.74", "117.74", "112.35", "0.543"
    "after 3 years", "99.43", "100.06", "0.634"
    "after 5 years", "91.39", "91.99", "0.661"


Water concentration at point :math:`x\mathrm{=}0.06`:


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", ":math:`\text{\%}` **difference**"
    "after 1 hour", "128.80", "128.80", "2.53 10-11"
    "after 3 days", "128.80", "128.80", "0.002"
    "after 28 days", "124.98", "125.67", "0.552"
    "after 1.25 years", "101.32", "102.42", "1.089"
    "after 3 years", "89.60", "90.64", "1.158"
    "after 5 years", "82.33", "83.27", "1.140"



Comments
------------

Here we check that the error committed is small since it is less than :math:`\text{1.5\%}`, which is entirely correct given the relatively crude time discretization used, especially at the end of the calculation.