26.2.1 Hanging Node Adaption

Grids produced by the hanging node adaption procedure are characterized by nodes on edges and faces that are not vertices of all the cells sharing those edges or faces, as shown in Figure  26.2.1.

Hanging node grid adaption provides the ability to operate on grids with a variety of cell shapes, including hybrid grids. Although the hanging node scheme provides significant grid flexibility, it requires additional memory to maintain the grid hierarchy which is used by the rendering and grid adaption operations.

Hanging Node Refinement

The cells marked for refinement are divided as described here:

• A triangle is split into 4 triangles.

• A quadrilateral is split into 4 quadrilaterals.

• A tetrahedron is split into eight tetrahedra. The subdivision consists of trimming each corner of the tetrahedron, and subdividing the enclosed octahedron by introducing the shortest diagonal.

• A hexahedron is split into 8 hexahedra.

• A wedge (prism) is split into 8 wedges.

• A pyramid is split into 6 pyramids and 4 tetrahedra.

Figures  26.2.2 and 26.2.3 illustrate the division of the supported cell shapes.

To maintain accuracy, neighboring cells are not allowed to differ by more than one level of refinement. This prevents the adaption from producing excessive cell volume variations (reducing truncation error) and ensures that the positions of the parent (original) and child (refined) cell centroids are similar (reducing errors in the flux evaluations).

Hanging Node Coarsening

The mesh is coarsened by reintroducing inactive parent cells (uniting the child cells to reclaim the previously subdivided parent cell). An inactive parent cell is reactivated if all its children are marked for coarsening. You will eventually reclaim the original grid with repeated application of the hanging node coarsening. Using the hanging node adaption process, you cannot coarsen the grid further than the original grid. However, conformal coarsening allows you to remove original grid points to reduce the density of the grid.

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