19.10.1 Geometry-Based Adaption Approach

Geometry-based adaption works on the principle of geometry reconstruction. In this approach, the cell count of the mesh is increased by creating the new nodes in the domain in between the existing nodes of the mesh. The newly created nodes are projected in such a way that the resulting mesh is finer and it's shape is closer to the original geometry.

The following sections explain how nodes are projected and the parameters that control the node propagation.

Node Projection

Consider a coarse mesh created for a circular geometry. A section of the mesh close to the circular edge is shown in Figure  19.10.1. The edge is not smooth and has sharp corners, because of which its shape is not closer to that of the original geometry. Using boundary adaption along with the geometry reconstruction option will result in a mesh with smoother edges as shown in Figure  19.10.2.

In Figure  19.10.2, the dotted lines represent the original edge of the mesh. The boundary adaption process creates new nodes in between the original nodes. These nodes are projected towards the edge of the geometry, because of which the resulting mesh has smooth edges and its shape is closer to the original geometry.

Only the nodes created in the adaption process (newly created nodes) are projected and the original nodes retain their positions.

Figure 19.10.1: Mesh Before Adaption

Figure 19.10.2: Projection of Nodes

The following parameters control node projection and are specified in Geometry Based Adaption dialog box.

• Levels of Projection Propagation: This parameter allows you to specify the number of node layers across which node propagation should take place for geometry reconstruction. A value of 1 means only the nodes at the boundary will be projected, a value of 2 means the nodes at the boundary and the nodes in the next layer will be projected, and so on.

  Note:   The nodes in the first level are projected by a maximum magnitude and the node in the last level are projected by a minimum magnitude. The magnitude of projection decreases gradually from the first level to the last level.

  For example, a value of 3 for Levels of Projection Propagation means, the level 1 node is projected by maximum magnitude and level 3 node is projected by minimum magnitude. Figure  19.10.3 illustrates the level of propagation and magnitude of projection of newly created nodes.

  Figure 19.10.3: Levels Projection Propagation and Magnitude

  

• Direction of Projection: This parameter allows you to specify the direction, X, Y, or Z (for 3D), for node projection. If you do not specify any direction, the node projection takes place at the nearest point of the newly created node.

• Background Mesh: This option allows you to use a fine surface mesh as a background mesh, based on which the geometry is reconstructed. When you read the surface mesh, the node projection will take place based on the node positions of the background mesh.

    This option is useful when the mesh you want to adapt is very coarse and geometry is highly curved. In such cases, node projection, only by specifying the parameters may not result in a good quality mesh. However, you can also modify the propagation criteria by specifying the parameters.

  You can read only one surface mesh at a time. The various zones of the surface mesh will be listed in the Background Mesh drop-down list.

Example of Geometry-Based Adaption

Consider a mesh created for a spherical geometry. The initial mesh is very coarse, because of which it has sharp corners (as in Figure  19.10.4). It does not represent the spherical geometry accurately. To recover the original spherical geometry from this coarse mesh use geometry-based adaption.

Figure 19.10.4: Coarse Mesh of a Sphere

If you adapt boundaries of the domain without activating the Reconstruct Geometry option, the resulting mesh (see Figure  19.10.5) has sufficient number of cells, but the boundary of the domain still contains sharp corners.

Boundary adaption only creates new nodes in between the existing nodes to increase the cell count of the mesh. Since it does not project the nodes, the shape of the mesh remains as it is.

If you adapt the boundary with Reconstruct Geometry option. The resulting mesh (Figure  19.10.6) has more number of cells and less sharp corners at boundary. In addition, the newly created nodes are projected in a direction such that it's shape is closer to the original geometry (i.e., sphere with smooth boundary).

Figure 19.10.5: Adapted Mesh Without Geometry Reconstruction

Figure 19.10.6: Mesh after Geometry-Based Adaption