B modeling
==============


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

We use Granger's law of diffusion


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
------------

We find exactly the same solution as Mensi's law.