Many physical problems exhibit strong gradients in specific directions compared to other directions. To successfully perform finite element analysis and obtain accurate solutions for such problems, elements in the finite element mesh must be small enough in these directions. Anisotropic meshes with small dimensions in the directions of strong gradients and large sizes along others can significantly reduce solution costs. This research focuses on two classes of problems requiring generation of such anisotropic tetrahedral meshes.

Viscous flow problems exhibit boundary layers and free shear layers in which the solution gradients, normal and tangential to the flow, differ by orders of magnitude. The Generalized Advancing Layers Method is presented here as a method of generating meshes suitable for capturing such flows. The method is designed to reliably generate anisotropic elements in boundary layers for arbitrarily complex non-manifold domains. The boundary layer mesh is created by tetrahedronization of prismatic, transition and blend polyhedra constructed on top of an initial surface mesh. The method includes several new technical advances allowing it to mesh complex geometric domains that cannot be handled by other techniques and is currently being used for simulations in the automotive industry.

Anisotropic meshes are also desirable in problems with a strongly non-linear solution across thin sections of the analysis domain. A procedure has been developed to transform an isotropic mesh with insufficient refinement through thin sections into one with a user defined number of elements through such sections. The method automatically identifies deficient portions of the mesh and anisotropically refines it using local mesh modification tools.

The two mesh generators form components of an overall framework for adaptive analysis in which anisotropic mesh generation and adaptation decrease the computational cost of converging to solutions of the desired accuracy for simulations in general geometric domains.