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26.2.2 Conformal Adaption

The conformal adaption process does not create hanging nodes. Instead, all the cells sharing an edge or face include all the nodes on those entities. The conformal refinement process adds nodes on edges and the conformal coarsening removes nodes and retriangulates the resulting cavity.

Note:   This process should not be used in conjunction with dynamic adaption (described in Section  26.5).



Conformal Refinement


To refine the cell, split the boundary or internal faces (including periodic boundary faces). This technique has two primary advantages:

Figure  26.2.4 shows how the triangle labeled $A$ would be split for refinement. The cells are refined by splitting the longest edge of the triangle or tetrahedron.

Figure 26.2.4: Cell Refinement by Bisecting Longest Edge
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The process is to find the longest edge of any cell marked for refinement search for a longer edge. If any of the neighbor cells has a longer edge, the scheme spins around that new edge searching for a longer edge. When the longest edge is identified, it is split. Although this process maintains the quality of the triangulation with repeated application, it splits many cells that are not marked for refinement.

For example, Figure  26.2.5 shows the original cell marked for refinement (marked with an X), and Figure  26.2.6 shows the final mesh created by the conformal refinement process.

Figure 26.2.5: Original Grid with Cell Marked for Refinement
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Figure 26.2.6: Final Grid after Conformal Refinement
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Conformal Coarsening


The grid is coarsened by removing nodes that are shared by cells marked for coarsening. If all the cells attached to the node are marked for coarsening, the solver attempts to remove the node. Local retriangulation process is attempted for each of the nodes marked for removal, as follows:

1.   A list of the cells attached to the marked node is generated. Removing these cells creates a cavity that must be retriangulated.

2.   A list of the faces inside the cavity is generated.

3.   A list of the faces on the cavity boundary is generated.

4.   If the node to be removed is on a boundary, a new boundary triangulation is generated. Those faces are added to the list of faces on the cavity.

5.   From the list of faces on the cavity, a new Delaunay triangulation is created. See the Theory chapter in the TGrid User's Guide for a description of Delaunay triangulation.

6.   If the process is successful, the node, faces, and cells from the original triangulation of the region are deleted.

7.   All nodes associated with the cavity are removed from the list of deleted nodes to avoid consecutive coarsening in the same region.

8.   The solution variables in the new cells are computed using a volume-weighted average.

Figure  26.2.7 illustrates the removal of node $n1$ and the resulting retriangulation. In this example, $ c1, c2, c3, c4,$ and $c5 $ are the cells attached to the node. Faces $ f6, f7, f8, f9,$ and $ f10 $ are the faces inside the cavity. Faces on the cavity includes $ f1, f2, f3, f4,$ and $f5 $. The new faces of the triangulation are $ f11 $ and $ f12 $, and the new cells are $ c6, c7,$ and $c8 $.

Figure 26.2.7: Removing a Node and Retriangulating the Region
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Nodes introduced by refinement are called refinement nodes. Nodes that existed in the mesh before refinement are called original nodes. By default, only refinement nodes can be removed in the coarsening process, but you can remove any node by resetting the node flags. For information on node flags, see Section  26.12.

Presently, the grid-coarsening facility is available only in the 2D version of FLUENT.


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© Fluent Inc. 2006-09-20