Reference problem
=====================


3D geometry
------------

The structure is a straight parallelepiped with a square base, its dimensions (see Figure) are as follows:

:math:`\mathit{Lx}=\mathrm{1m}`, :math:`\mathit{Ly}=\mathrm{1m}`, and :math:`\mathit{Lz}=\mathrm{5m}`

The interface is defined by level sets directly in the command file using the DEFI_FISS_XFEM [:ref:`U4.82.08 <U4.82.08>`] operator. It is introduced in the middle of the structure by an equation level set :math:`\mathit{LSN}` (see Figure):

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


.. image:: images/10000000000002C2000004407D5FFE3DE81AA07F.png
    :width: 2.2953in
    :height: 3.5433in


.. _RefImage_10000000000002C2000004407D5FFE3DE81AA07F.png:

Figure 1.1-1: Bar geometry and interface positioning


2D geometry
------------

The structure is a rectangle; its dimensions (see Figure) are as follows:

:math:`\mathit{Lx}=\mathrm{1m}` and :math:`\mathit{Ly}=\mathrm{5m}`

The interface is defined by level sets directly in the command file using the DEFI_FISS_XFEM [:ref:`U4.82.08 <U4.82.08>`] operator. It is introduced in the middle of the structure by an equation level set :math:`\mathit{LSN}` (see Figure):

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


.. image:: images/1000000000000268000003E8718D1684009183FC.png
    :width: 2.1815in
    :height: 3.5433in


.. _RefImage_1000000000000268000003E8718D1684009183FC.png:

Figure 1.2-1: Bar geometry and interface positioning


Material properties
----------------------


* :math:`\lambda \mathrm{=}1W\mathrm{.}{m}^{\mathrm{-}1}°{C}^{\mathrm{-}1}`


* :math:`\rho {C}_{p}=2J/{m}^{-3}°{C}^{-1}`


Boundary conditions and loads
-------------------------------------

A temperature :math:`\text{}\stackrel{̄}{T}{\text{}}^{\text{inf}}=10°C` is imposed on the knots at the lower edge of the bar, and :math:`\text{}\stackrel{̄}{T}{\text{}}^{\text{sup}}=20°C` on the knots at its upper edge.


Initial conditions
--------------------

None (the problem is stationary)


.. _RefNumPara__2359_165696795: