D modeling
==============


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

AXIS_FOURIER **(QUAD4)**


.. image:: images/100007C60000217D00000DF44B498962CCBA31C9.svg
    :width: 432
    :height: 180


.. _RefImage_100007C60000217D00000DF44B498962CCBA31C9.svg:

The mesh description axes are :math:`x(r)` and :math:`y(z)`.

Fashion - Fourier: 2 :math:`T(A)=0.`


.. csv-table::

    ":math:`S=0.` ", "all over the domain"
    ":math:`[\mathrm{BC}]`:", ":math:`\phi =2.`"
    ":math:`[\mathrm{CD}]`:", ":math:`h=2.` :math:`{T}_{\mathrm{ext}}=2.`"



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

Number of knots: 153

Number of meshes and types: 100 QUAD4


notes
---------

Since the Fourier mode number does not affect the load, the MODE_FOURIER keyword is not required in the CALC_VECT_ELEM command.


Tested values
---------------


.. csv-table::

    "**Identification**", "**Reference**"
    ":math:`T(B)` ", "1."
    ":math:`T(C)` ", "1."
    ":math:`T(D)` ", "1."
    ":math:`T(F)` ", "0.25"
    ":math:`T(G)` ", "0.25"
    ":math:`{\phi }_{r}(B)` ", "—2."
    ":math:`{\phi }_{r}(C)` ", "—2."
    ":math:`{\phi }_{r}(D)` ", "—2."
    ":math:`{\phi }_{r}(F)` ", "—1."
    ":math:`{\phi }_{r}(G)` ", "—1."
    ":math:`{\phi }_{\theta }(B)` ", "2."
    ":math:`{\phi }_{\theta }(C)` ", "2."
    ":math:`{\phi }_{\theta }(D)` ", "2."
    ":math:`{\phi }_{\theta }(F)` ", "1."
    ":math:`{\phi }_{\theta }(G)` ", "1."
    ":math:`{\phi }_{z}(B)` ", "0."
    ":math:`{\phi }_{z}(C)` ", "0."
    ":math:`{\phi }_{z}(D)` ", "0."
    ":math:`{\phi }_{z}(F)` ", "0."
    ":math:`{\phi }_{z}(G)` ", "0."



notes
---------

The poor precision recorded on :math:`{\phi }_{r}(B)`, :math:`{\phi }_{r}(C)`, :math:`{\phi }_{r}(D)` is explained by the fact that :math:`B`, :math:`C`, and :math:`D` are edge nodes, so the flows are not averaged over adjacent elements in the direction of the temperature gradient (r direction).

This phenomenon is not found on :math:`{\phi }_{\theta }`, because :math:`{\phi }_{\theta }` is weighted by :math:`1/r`.