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Traditionally, adding cells to a mesh, known as H-refinement, was the primary means by which solution accuracy could be improved. The additional resolution enables the capturing of flow phenomena often diffused by coarser variations of the same mesh. Another technique used to improve spatial and temporal accuracy is by performing degree elevation, both for the assumed solution within a given element and for the element itself, and is called high order (HO) meshing. In doing so, linear meshes can become curved with the addition of nodes along edges, faces, and in the interior. Fewer elements are then required to accurately represent curved geometry and capture complex flow features of interest.
** While characterizing an HO mesh, it is important to note that its order is equal to its polynomial degree plus one. Therefore, a linear mesh has degree 1 and order 2, a quadratic mesh has degree 2 and order 3, etc.
A sphere is meshed with layers of anisotropic cells clustered toward the sphere's surface that transition to an isotropic far-field tetrahedral mesh. Meshes of three cell types (only tetrahedra, prisms and tetrahedra, and mixed elements) and four polynomial degrees (linear, quadratic, cubic, and quartic) are generated.
Figure 1. P1 meshes in the top row, and P2 meshes in the bottom row.
2. Wing-Only Geometry
A HO mesh was generated on a wing-only geometry from the 3rd AIAA Drag Prediction Workshop (DPW). To keep the number of degrees of freedom relatively constant, the number of cells in the original linear mesh decreased as the polynomial degree increased in order. The volume mesh consists of layers of anisotropic cells near the surface that transition to isotropic tetrahedra in the far field.
Figure 2. Close-up views of the DPW 3 wing surface mesh, tip region, and leading edge. Clockwise from the upper left: P1, P2, P4, and P3.
3. ROBIN Fuselage
A generic ROBIN fuselage was meshed with Pointwise and then elevated to a P2 mesh. Two linear meshes and two P2 meshes were created, and the goal was to have approximately the same number of nodes in the P1 and P2 mesh for each coarse and fine version.
Figure 3. P1 (top row) and P2 (bottom row) fine and coarse surface meshes for the ROBIN fuselage.
4. Aircraft Nose Landing Gear Configuration
An aircraft nose landing gear configuration from the 3rd AIAA Workshop on Benchmark Problems for Airframe Noise Computations is used for high-order mesh generation. A coarse linear mesh of the configuration is elevated to P2 using the Fidelity Pointwise software.
Figure 4. BANC III landing gear mesh with inserted P2 nodes (left), close-up view of BANC III P2 mesh (right).
5. NASA CRM Wing-Body
The NASA Common Research Model of a wing-body configuration from the sixth AIAA CFD Drag Prediction workshop is used in this study. The coarse resolution, the linear, unstructured tetrahedral mesh is used as the basis for P2 and P3 high-order meshes. A new surface mesh consisting of mixed elements is generated and serves as the basis for a P4 mesh.
Figure 5. Axial cut through a P2 mesh for the DPW6 CRM wing-body configuration near the wing tip trailing edge (left), cut through the P3 mesh for the DPW 6 wing-body configuration near the tail indentation (center), a mixed element P4 mesh for the DPW6 wing-body configuration (right).
Watch the YouTube video below to learn about High Order Mesh Setup with Fidelity Pointwise: -
Steve L. Karman, J. Taylor Erwin, Ryan S. Glasby, and Douglas L. Stefanski, “High-Order Mesh Curving Using WCN Optimization,” AIAA paper no. 2016-3178, June 2016.
To learn more about High-Order meshing using Fidelity Pointwise, click the button below: -