Anisotropic sources for surface and volume boundary layer mesh generation

• Published in: Journal of computational physics Vol. 424; p. 109855
• Main Authors: Aubry, R., Dey, S., Mestreau, E.L., Williamschen, M., Szymczak, W.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.01.2021; Elsevier Science Ltd
• Subjects: Algorithms; Anisotropic sources; Anisotropy; Boundary layer; Boundary layers; Computational physics; Finite element method; Mathematical analysis; Mesh generation; Sizing; Sizing field; Smoothness; Tensors; Volume mesh generation; Volume mesh generation; Anisotropic sources; Sizing field; Boundary layer
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.109855

•Model the boundary layer within the anisotropic sizing field.•Couple surface and volume meshing.•Provide a parameter to control anisotropy strength.•Build a smooth mesh by construction. A new approach to model and compute the metric tensor corresponding to a-priori prescribed surface and volume boundary layers is presented. This is achieved by the use of sources that model the combined anisotropic metric. Algorithms are presented to both evaluate the resulting metric value at any point in space and the efficient approximation of the minimum and maximum metric over an axis-aligned box which enables fast evaluation of the anisotropic metric independent of the approach used for mesh generation. The ability to model and evaluate the anisotropic sizing independently ensure that mesh generation algorithms that use it can produce meshes that correctly and predictably capture the sizing fields induced by the user prescribed boundary layer attributes. The method is unique in producing globally smooth representations of the final anisotropic metric including the influence of implicit anisotropy due to boundary curvature and any prescribed isotropic sizes. As a result, it addresses robustness and size smoothness issues in legacy approaches that decouple the surface and volume mesh generation stages. The value of the new method is demonstrated by several examples that include both surface and volume boundary layers prescribed on geometries with curved boundaries.