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


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

The modeling used is D_ PLAN_HMS. The duration of the simulation is set to :math:`{T}_{1}\mathrm{=}0.1s` with 10 steps of time.


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

2048 TRIA6 stitches.


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

The values of the numerical solution are tested at the final moment :math:`{T}_{1}\mathrm{=}0.1s` in 3 nodes.


+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|**Node name**       |:math:`X` **(** :math:`m` **)**|:math:`Y` **(** :math:`m` **)**|**Analytical solution**         |**Relative error**|
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|:math:`\mathit{N25}`|0.75                           |0.75                           |PRE1                   |4.53E-1 |0.7%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|                    |                               |                               |DX                     |7.21E-2 |0.2%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|                    |                               |                               |DY                     |7.21E-2 |0.2%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|:math:`\mathit{N40}`|0.875                          |0.125                          |PRE1                   |1.33E-1 |0.75%             |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|                    |                               |                               |DX                     |5.10E-2 |0.2%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|                    |                               |                               |DY                     |-5.10E-2|0.2%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|:math:`\mathit{N35}`|0.375                          |0.625                          |PRE1                   |7.73E-1 |0.8%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|                    |                               |                               |DX                     |-5.10E-2|0.2%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+
|                    |                               |                               |DY                     |5.10E-2 |0.2%              |
+--------------------+-------------------------------+-------------------------------+-----------------------+--------+------------------+

**Table** 3.3-1


notes
---------

The numerical results are in very good agreement with the analytical results.