Local Refinement of Hexahedra to Improve the Wake Discretisation

3.2.1 Key Features of the Local Hexahedra Refinement Method

To locally refine a hexahedral layer, hanging nodes and faces have to be introduced into the grid. This means that the grid conformity has to be given up. If a solver does not handle hanging entities, the grid has to be made conform by decomposing the hanging relations. This is achieved by decomposing hexahedra facing a hanging entity into prisms or into pyramids and tetrahedra. For the TAU-Solver this task is done by the tool make_conform.

As a result, parent hexahedra have to be decomposed into child hexahedra in order to achieve a local refinement. A parent hexahedron can be decomposed in either two, four or eight child hexahedra. For a TAU-grid this means that the child hexahedra are introduced into the grid and the parents are deleted. Thereby, the hanging relations are introduced.

Due to limitations of make_conform a parent is allowed to faec on up to a maximum of four child hexahedra. Furthermore, the implementation of this TAU – tool is limited to 3D grids.

As a result of this, the following procedure was established for the present local hexahedra refinement tool, called hexfine. Hexahedra destined for refinement by user-input are marked. The child hexahedra of all marked hexahedra are generated. These child hexahedra are constituted by the corner points as well as the face and edge midpoints of the parents. To maintain the smoothness of the grid, the curvatures of the initial grid have to be reconstructed. For this purpose, the face, edge and volume midpoints are interpolated via a bicubic or a tricubic spline. The newly generated children are added to the coordinates and point lists of the grid. The par­ents are removed. So far the procedure yields a grid with hanging entities which is not TAU-conform. In case of 3D grids, no further steps are necessary and the

Fig. 20 Schematic illustration of the process to decomposing hanging nodes and faces
grid can be stored. Applying make_conform on the stored grid will give a TAU- conform grid.

In case of 2d grids, the hanging relations have to be decomposed by hexfine itself. This is done by decomposing hexahedra facing hanging entities into a prism and two hexahedra (cf. Figure 20). This type of decomposition yields a TAU-conform grid. Running make_conform is therefore not necessary for 2D grids.