K modeling
==============


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

A non-linear 3D thermal modeling is used.

This modeling tests the creation of empirical thermal modes by incremental POD.
Parameters are taken in such a way as to find the same modes as in modeling A.


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

The mesh contains 27 elements of type HEXA8.


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

We test some values of the primal base (as they are empirical modes, the tests are*
done at the nearest sign):


.. csv-table::

    "**Identification**", "**Reference type**"
    "Point :math:`A` - TEMP -Mode 1"," NON_REGRESSION"
    "Point :math:`A` - TEMP -Mode 2"," NON_REGRESSION"
    "Point :math:`A` - TEMP -Mode 3"," NON_REGRESSION"


We test some values of the dual base (as they are empirical modes, the tests are
done to the nearest sign):


.. csv-table::

    "**Identification**", "**Reference type**"
    "Point :math:`A` - FLUX_NOEU/FLUX - Mode 1"," NON_REGRESSION"
    "Point :math:`A` - FLUX_NOEU/FLUY -Mode 1"," NON_REGRESSION"
    "Point :math:`A` - FLUX_NOEU/FLUX - Mode 2"," NON_REGRESSION"
    "Point :math:`A` - FLUX_NOEU/FLUY -Mode 2"," NON_REGRESSION"
    "Point :math:`A` - FLUX_NOEU/FLUX - Mode 3"," NON_REGRESSION"
    "Point :math:`A` - FLUX_NOEU/FLUY -Mode 3"," NON_REGRESSION"


We test the values of the reduced coordinates (table COOR_REDUIT) :math:`{a}_{m}^{T}` calculated
when extracting empirical modes. For the primal base (temperature):


.. csv-table::

    "**Identification**", "**Instant**", "**Mode**", "**Reference type**"
    ":math:`{a}_{m=1,t=10s}^{T}` "," :math:`t=10s` ", "1"," NON_REGRESSION"
    ":math:`{a}_{m=1,t=4s}^{T}` "," :math:`t=4s` ", "1"," NON_REGRESSION"
    ":math:`{a}_{m=3,t=10s}^{T}` "," :math:`t=10s` ", "3"," NON_REGRESSION"
    ":math:`{a}_{m=3,t=4s}^{T}` "," :math:`t=4s` ", "3"," NON_REGRESSION"


For the dual base (heat flow :math:`{\Phi}`):


.. csv-table::

    "**Identification**", "**Instant**", "**Mode**", "**Reference type**"
    ":math:`{a}_{m=1,t=10s}^{{\Phi}}` "," :math:`t=10s` ", "1"," NON_REGRESSION"
    ":math:`{a}_{m=1,t=4s}^{{\Phi}}` "," :math:`t=4s` ", "1"," NON_REGRESSION"
    ":math:`{a}_{m=4,t=10s}^{{\Phi}}` "," :math:`t=10s` ", "4"," NON_REGRESSION"
    ":math:`{a}_{m=4,t=4s}^{{\Phi}}` "," :math:`t=4s` ", "4"," NON_REGRESSION"



notes
---------

The calculated modes are strictly identical between POD and POD incremental.