J modeling
==============

This modeling is based on all the characteristics of the 2D reference problem described on page :ref:`2 <RefNumPara__3514_276907781>`., except that axisymmetric modeling is considered. It is therefore a cylindrical bar, but the analytical solution described on page :ref:`4 <RefNumPara__2359_165696795>` remains valid for this problem.


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

For this modeling, the bar is cylindrical and its dimensions are as follows:


* radius :math:`\mathit{Lx}=\mathrm{0,5}m`


* height :math:`\mathit{Ly}=\mathrm{5m}`

The interface is introduced halfway up the bar by a level set :math:`\mathit{LSN}` equation:

:math:`\mathit{LSN}`: :math:`y`

We use the AXIS model of the THERMIQUE phenomenon.


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

The mesh includes 5 TRIA3 meshes.


.. image:: images/10000201000000EB0000023FF4A3DC63BDBE1701.png
    :width: 1.2165in
    :height: 2.9807in


.. _RefImage_10000201000000EB0000023FF4A3DC63BDBE1701.png:

Figure 12.2-1: J mesh


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

We first test the values of the classical degrees of freedom TEMP and Heaviside H1 of the temperature field at the output of the THER_LINEAIRE operator, at the nodes located just below (2 knots) and above the interface (2 nodes).


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "All nodes just above the interface - :math:`\mathit{TEMP}` ", "'ANALYTIQUE'", "''", "20"," 0.1%"
    "All nodes just below the interface - :math:`\mathit{TEMP}` ", "'ANALYTIQUE'", "''", "10"," 0.1%"
    "All nodes located just below/above the interface - :math:`\mathit{H1}` ", "'ANALYTIQUE'", "5"," 0.1%"


We then test the value of the degree of freedom TEMP of the temperature field at the outlet of POST_CHAM_XFEM, at the nodes located just below and above the interface.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "All nodes just below the interface - :math:`\mathit{TEMP}` ", "'ANALYTIQUE'", "''", "10"," 0.1%"
    "All nodes located just above the interface :math:`\mathit{TEMP}` -", "'ANALYTIQUE'", "20"," 0.1%"


Finally, we test the value of the TEMP component of the TEMP_ELGA field on the Gauss points located below and above the interface (*cf.* note page 6).


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "On the Gauss points below the interface - :math:`\mathit{TEMP}` ", "'ANALYTIQUE'", "''", "10"," 0.1%"
    "On the Gauss points above the interface - :math:`\mathit{TEMP}` ", "'ANALYTIQUE'", "''", "20"," 0.1%"