Hex-Core Voxel Meshes: The Best of Structured and Unstructured Meshing

(Steinbrenner, Wyman, Jefferies, Karman, & Shipman, 2020)

Mesh generation is vital to computational fluid dynamics (CFD) research and applications, enabling the numerical analysis of fluid flow around complex geometries. Historically, the meshing process has alternated between structured and unstructured methods, each with its unique advantages and limitations. However, the recent advent of hex-core voxels represents a significant leap forward, blending the best of both worlds to offer a superior meshing methodology.

Limitations of Traditional Meshing Methods

Structured (mapped) grids were once the gold standard in CFD, prized for their high quality and flow solution accuracy. Yet, as the complexity of geometries under investigation expanded, the time and level of expertise required to construct suitable multi-block structured grids became a cumbersome bottleneck. This challenge spurred the development and adoption of unstructured tetrahedral (tet) meshes, which offered a higher degree of automation and faster turnaround.

However, this convenience came at a cost: tetrahedral meshes required more cells to achieve comparable levels of accuracy as structured meshes and were less accurate. The increased cell count could be time-intensive and computationally expensive to generate. Additionally, the lack of cell face alignment with the primary flow direction in tet meshes often lead to higher error estimates and less accurate results than obtained with structured meshes.  

The Rise of Hex-Core Voxels

Hex-core voxel meshes in Cadence Fidelity Pointwise mesh generation represent a significant advancement in addressing the drawbacks of unstructured tet meshes. Hex-core voxels combine the automation and flexibility of unstructured meshing with the quality and accuracy benefits of structured grids. This hybrid approach begins with a small number of root voxel elements, which are refined through an octree framework to meet specific size field specifications. The voxel elements are classified based on their relation to the surface mesh.

Transition pyramids (yellow) and tets (red) connecting levels of hex refinement (Steinbrenner, Wyman, Jefferies, Karman, & Shipman, 2020)

Binary and Octree Structures

The underlying data structures of hex-core voxels—binary and octree structures—play a crucial role in their efficiency and effectiveness. An octree is a type of tree data structure where every internal node precisely contains eight child nodes. This hierarchical organization of nodes, similar to a binary tree but with eight children instead of two, offers a more compact and efficient representation, especially for 3D spaces. By reducing the number of pointers required and simplifying the encoding of node locations, octrees facilitate a more streamlined and scalable approach to voxel meshing (Steinbrenner, Wyman, Jefferies, Karman, & Shipman, 2020).

Isotropic Hex Core Meshes

One key benefit of hex-core voxel meshes is their ability to avoid the geometric randomness prevalent in tetrahedral meshes. By replacing isotropic tets with Cartesian-aligned hex cubes or voxels, these meshes can more effectively resolve near-body phenomena and better manage gradients in off-body regions (Steinbrenner, Wyman, Jefferies, Karman, & Shipman, 2020). This capability is particularly valuable in CFD applications, where accurate modeling of fluid flow is critical.

Implementation Modes

Hex-core voxel meshing can be implemented in several modes, each tailored to specific meshing requirements. In the "external" mode, the user defines block extents, and surface meshes are inserted to create a conformal mesh that includes both exterior and interior elements. This mode is particularly useful for simulating flow around complex geometries.

External-mode voxel mesh (left), internal-mode voxel mesh(right) (Steinbrenner, Wyman, Jefferies, Karman, & Shipman, 2020)

The "internal" mode, on the other hand, involves forming voxels within a prescribed outer boundary, accommodating both internal flow geometries and complex boundary conditions. This mode is beneficial for simulating flow within complex geometries. These versatile implementation modes underscore the adaptability of hex-core voxel meshes to a wide range of CFD applications (Steinbrenner, Wyman, Jefferies, Karman, & Shipman, 2020).

Once the root dimensions and extent box are computed, root voxels are refined recursively to match the local size field.

Latest Update in Fidelity Pointwise Hex Core Voxel Meshing

With Fidelity Pointwise 2023.1, users now have an option during CAE export to recombine the tetrahedra and pyramids in the voxel transition regions back into hex-shaped polyhedra. If Poly-Voxel export is enabled, a secondary option is available that enhances the face orthogonality of the poly cells by offsetting the center nodes of the hex faces. Testing indicated that this option provided a slight improvement in convergence. Currently, Poly Voxel export supports seven different CAE formats.

Future of Mesh Generation

The introduction of hex-core voxels represents a significant evolution in mesh generation technology. By combining the structural advantages of structured grids with the automation and flexibility of unstructured methods, hex-core voxels offer a compelling solution to the challenges of meshing complex geometries. As this technology continues to mature and gain adoption, it holds the promise of further enhancing the accuracy, efficiency, and scope of CFD research and applications.

References

Steinbrenner, J. P., Wyman, N. J., Jefferies, M. S., Karman, S. L., & Shipman, J. (2020). Implementation of a Size Field Based Isotropic Hex Core Meshing Algorithm. AIAA Scitech 2020 Forum. Orlando, Florida: AIAA 2020-1408. doi:10.2514/6.2020-1408

Learn more about Hex-Core Voxels in this article - Hex-Core Voxels for Near-Body and Off-Body Meshing in Fidelity Pointwise

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