chapter  11
69 Pages

Mesh Generation

WithJuan C. Heinrich, Darrell W. Pepper

Mesh (or grid) generation establishes the locations of nodal (or grid) points, element connectivities, and specification of boundary values, i.e., prescribed Dirichlet and Neumann conditions for a specific problem. A physical problem domain (or region) must be discretized by the user, and a solution achieved using node points within either the physical or computational domain. Some numerical models require the use of structured (or ordered) meshes, which must be orthogonal. If the physical domain is rectangular, the mesh is easy to construct; if the domain is irregular, or highly distorted, a transformation must first be made to create a rectangular, computational domain. This type of procedure is common to finite difference (or finite volume) methods and accounts for the popular use of boundary-fitted coordinates (BFC); the physical problem is globally transformed to a rectangular geometry. The FEM requires no such constraint and operates by utilizing unstructured meshes, i.e., orthogonality is not necessary. Each element is individually treated by performing a local isoparametric transformation (from x,y to ξ,η space), calculations are made and stored, then the procedure is repeated for the next element, not necessarily in sequence.