E modeling
==============


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

Method GEOMETRIQUE is used by PROPA_FISS to update the crack position. A **auxiliary grid** is used to represent level-sets. This makes it possible to test the use of this method under the same conditions as those of method UPWIND (C modeling) for a direct comparison.

The same model as that described for modeling A is used.


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

We use the same mesh as that of modeling A. We use the same auxiliary grid as that of modeling C.


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

The position of the crack bottom cannot be recovered in the command file and therefore it is not possible to check directly whether the solution calculated by method GEOMETRIQUE is consistent with the reference solution. However, it can be verified that the crack bottom is in the same element as that which contains the crack bottom of the reference solution. In fact, the distance between the crack background and each node of this element is given by the value of the level sets and we can say that the crack background is contained in the element if the value of the level sets on these nodes is less than the length of the largest edge of the element.

The reference element nodes are :math:`\mathrm{N304}`, :math:`\mathrm{N1040}`, and :math:`\mathrm{N1512}`. The length of the element's longest edge is :math:`2.0\mathrm{mm}`. This value is used as a tolerance on the value of the level sets.

The value of the level sets at each node can be retrieved from the command file using the POST_RELEVE_T operator:


.. csv-table::

    "**Knot**", "**LSN**
    [:math:`\mathrm{mm}` **]**", "**LST**
    [:math:`\mathrm{mm}` **]**"
    ":math:`\mathit{N304}` ", "-0.757", "-1.356"
    ":math:`\mathit{N1040}` ", "1.213", "-1.844"
    ":math:`\mathit{N1512}` ", "0.847", "-0.321"



notes
---------

All tested values respect the tolerance used. This means that the position of the crack bottom calculated by method GEOMETRIQUE with the auxiliary grid is very close to that of the reference.