Mesh Generation
Mesh generation partitions a geometry into elements or cells on which a discretization is built, balancing fidelity, quality, and count.
Turning geometry into a grid
Before any finite element, volume, or difference method can run, the physical domain must be divided into a mesh of cells or elements that fill it without gaps or overlaps. Mesh generation is the process of creating this partition from a geometric description of the domain, and it strongly influences the accuracy, stability, and cost of the subsequent simulation. A poor mesh can corrupt an otherwise excellent solver.
Meshes are broadly structured or unstructured. Structured meshes have a regular connectivity (each interior node has the same number of neighbors), which yields efficient, cache-friendly solvers but limits geometric flexibility. Unstructured meshes allow arbitrary connectivity, fitting complex shapes at the cost of storing explicit connectivity.
Element types and methods
Common elements are triangles and quadrilaterals in two dimensions, tetrahedra and hexahedra in three. Delaunay triangulation and advancing-front methods generate unstructured simplex meshes; block-structured and multiblock techniques stitch structured patches across complex domains; hexahedral meshing is prized for accuracy but hard to automate for intricate geometry.
Boundary layers and adaptivity
Regions with steep gradients, such as boundary layers and material interfaces, need anisotropic elements stretched along the feature and refined across it. Mesh generation must also represent curved boundaries faithfully, using higher-order (curved) elements where linear facets would introduce geometric error. Adaptive generation refines the mesh where solution error demands it.
- Structured meshes: regular, efficient, geometrically limited
- Unstructured meshes: flexible, explicit connectivity
- Delaunay, advancing-front, and multiblock techniques
- Anisotropic elements for boundary layers and interfaces
In fusion device modeling, meshes must resolve shaped plasma boundaries, thin blanket and wall layers, and coil geometry, often using flux-aligned or field-aligned meshes so that the grid follows the anisotropy of magnetized transport.