Reference solution
=====================


Calculation method
-----------------

The reference results are either non-regression values (values of empirical modes, reduction coefficients) or values (displacements, temperatures, stresses and flows) calculated on a **complete** model.

Reduced coordinates are also tested. We recall that empirical trends :math:`{\mathrm{\Psi }}_{m}(x)` are such that:

.. math::
 :label: eq-1

    u (x, t)\ approx\ sum _ {m=1} ^ {\ mathit {nbmode}} {\ mathrm {\ Psi}} _ {m} (x)\ times {a} _ {m} (t)

For a given :math:`u(x,t)` field (temperature, displacement, heat flow, or stress) with :math:`{a}_{m}` the reduced coordinates.


.. _RefHeading__163478_637747685:


Reference quantities and results
-----------------------------------

For thermal, the results on the **complet** model:


.. csv-table::

    "**Location**", "**Moment**", "**Temperature (** TEMP **)**"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=1s` "," :math:`\mathrm{29,9053048593}°C`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=4s` "," :math:`\mathrm{139,462715634}°C`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=7s` "," :math:`\mathrm{567,08693147}°C`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` "," :math:`\mathrm{999,349943608}°C`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=1s` "," :math:`\mathrm{29,90499961}°C`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=4s` "," :math:`\mathrm{139,458066818}°C`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=7s` "," :math:`\mathrm{567,040457129}°C`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=10s` "," :math:`\mathrm{999,12502482}°C`"



.. csv-table::

    "**Location**", "**Moment**", "Flow **(** FLUX_NOEU **)**"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=7s` "," :math:`-\mathrm{0,0005673343795326032}W`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` "," :math:`-\mathrm{0,003152488515227189}W`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=7s` "," :math:`\mathrm{0,0011356797075429094}W`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=10s` "," :math:`0.0063191212851786W`"


For mechanics, the results on the **complet** model:


.. csv-table::

    "**Location**", "**Moment**", "**Component**", "**Move (** DEPL **)**"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` ", "DX", ":math:`\mathrm{0,0696319525128}\,{mm}`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` ", "DY", ":math:`\mathrm{0,199062276741}\,{mm}`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` ", "DZ", ":math:`\mathrm{0,529606351907}\,{mm}`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=10s` ", "DX", ":math:`-\mathrm{0,208992921588}\,{mm}`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=10s` ", "DY", ":math:`-\mathrm{0,208992921588}\,{mm}`"
    "Node B in :math:`(\mathrm{3,3,3})` "," :math:`t=10s` ", "DZ", ":math:`\mathrm{0,547254495773}\,{mm}`"



.. csv-table::

    "**Location**", "**Instant**", "**Component**", "**Constraint (** SIEF_NOEU **)**"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` "," SIXX "," :math:`-\mathrm{2739,13961277}\,{MPa}`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` "," SIYY "," :math:`-\mathrm{2737,51235419}\,{MPa}`"
    "Node A in :math:`(\mathrm{1,0,3})` "," :math:`t=10s` "," SIZZ "," :math:`-\mathrm{2612,22311229}\,{MPa}`"
    "Node C in :math:`(\mathrm{0,0,0})` "," :math:`t=10s` "," SIXX "," :math:`\mathrm{13992,3974341}\,{MPa}`"
    "Node C in :math:`(\mathrm{0,0,0})` "," :math:`t=10s` "," SIYY "," :math:`\mathrm{13992,3974341}\,{MPa}`"
    "Node C in :math:`(\mathrm{0,0,0})` "," :math:`t=10s` "," SIZZ "," :math:`\mathrm{14047,6477194}\,{MPa}`"
    "D knot in :math:`(\mathrm{3,1,0})` "," :math:`t=10s` "," SIXX "," :math:`\mathrm{13300,4780377}\,{MPa}`"
    "D knot in :math:`(\mathrm{3,1,0})` "," :math:`t=10s` "," SIYY "," :math:`\mathrm{13300,3220671}\,{MPa}`"
    "D knot in :math:`(\mathrm{3,1,0})` "," :math:`t=10s` "," SIZZ "," :math:`\mathrm{13368,1442621}\,{MPa}`"



Uncertainty about the solution
----------------------------

The error in the solution depends on the degree of reduction (number of empirical modes and size of the reduced domain).