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


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

We use non-linear thermal 3D modeling with hyper-reduction of the model. This
modeling tests the accuracy of the empirical modes obtained in modeling A on the
reduced domain created in modeling B.

We therefore use the bases produced in modeling A and the reduced domain created in
modeling B. The reconstruction operator REST_REDUIT_COMPLET is also tested by gappy- POD.


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

The mesh contains 27 elements of type HEXA8.


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

We test the value of the temperatures obtained with a hyper-reduced model compared to those
obtained in the complete model (U modeling):

.. csv-table::

    "**Location**", "**Instant**", "VALE_REFE **,"** (**TEMP**) **", "** PRECISION **"
    "Node A in :math:`({1,0,3})` "," :math:`t=1s` "," "," :math:`{29,9053048593}°C` ", "5.0E-5"
    "Node A in :math:`({1,0,3})` "," :math:`t=4s` "," "," :math:`{139,462715634}°C` ", "1.5E-5"
    "Node A in :math:`({1,0,3})` "," :math:`t=7s` "," "," :math:`{567,08693147}°C` ", "5.0E-6"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` "," "," :math:`{999,349943608}°C` ", "5.0E-6"


Node B does not belong to the reduced domain RID. We can therefore not access its value at the end.
hyper-reduced thermal calculation. We use operator REST_REDUIT_COMPLET:

.. csv-table::

    "**Location**", "**Instant**", "VALE_REFE **,"** (**TEMP**) **", "** PRECISION **"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` "," "," :math:`{999,12502482}°C` ", "0.3%"


And for flows:


.. csv-table::

    "**Location**", "**Instant**", "VALE_REFE **,"** (**FLUX_NOEU**) **", "** PRECISION **"
    "Node A in :math:`({1,0,3})` "," :math:`t=7s` "," :math:`-{0,00056733}W` "," 24%"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` "," "," :math:`-{0,00315249}W` ", "7.4%"
    "Node B in :math:`({3,3,3})` "," :math:`t=7s` "," :math:`{0,00113568}W` "," 40%"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` "," "," :math:`{0,00631912}W` ", "9.9%"



notes
---------

We see that the base produced in modeling A on the reduced domain of modeling B
makes it possible to obtain very good results (error less than 0.01%) compared to the complete calculation.
But they are necessarily slightly worse than in the simply reduced case (modeling C).

In addition, the reconstruction operator REST_REDUIT_COMPLET also gives a good solution to
0.3% close on the temperature rated outside of RID.

The values are less good for flows, due to their very low absolute value.