adding mesh tally amalgamation algorithm

[magnoxemo]

Description

Libmesh only supports isotropic refinement which means if there is a bigger quad element it be eight smaller quad in the next step (for AMR ). But there are cases where we might want to do tally in a complex shape element. This is basically treating a part some of the smaller elements to be treated one bin.

Algorithm

Now let's say I have a mesh that looks like this

+---------------+
|    a    |  c  |
|------   |----
|    b    |  d  |
+--------------+

But our clustering algorithm wanted to treat a, b, d together as one single element and changed their extra element integer id to 0 ( as a is the first element which' element id = 0 ).

+-----------------+
|     a   |    c |
|         |----  |
|    b        d  |
+----------------+

From openmc side, every time a collision happens in a, b or d we can just check

if ( cluster_id != -1 ){
   # that means part of a cluster 
    bin = get_bin_from_element( mesh.elem_ptr( cluster_id ) )
}

That mean all the scores in a, b and d gets accumulated in a (even though b and d will remain zero but we can fill the solution later ). Then open mc transfer the solution to cardinal. where we can do,

if ( cluster_id != -1 ){
   # that means part of a cluster 
   #get the first element in that cluster 
   first_element_in_that_cluster = get_score_from_element( mesh.elem_ptr( cluster_id ) )

   #get score from the first element 
   tally_score = get_score (first_element_in_that_cluster)

   #store the result in the current element 
   fill_aux_variable( _current_element)
}

But another concern we are reconstructing the raw tally to any meaning full score we need to normalize it and divide it by the volume, in this case $v_a+ v_b + v_d$ so need to adjust that here as well.

This over all design is dependable with cardinal frame work.