Smooth anisotropic sources with application to three-dimensional surface mesh generation

• Published in: Engineering with computers Vol. 32; no. 2; pp. 313 - 330
• Main Authors: Aubry, R., Dey, S., Karamete, K., Mestreau, E.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.04.2016; Springer Nature B.V
• Subjects: Anisotropy; Boundary layer; Boundary layer transition; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Curvature; Filtration; Intersections; Math. Applications in Chemistry; Mathematical analysis; Mathematical and Computational Engineering; Mesh generation; Original Article; Sizing; Smoothness; Systems Theory; Anisotropic sources sizing function; Anisotropic metric; Anisotropic mesh generation; Size distribution; Lower-envelope diagram
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-015-0420-3

Isotropic sources are extended to take anisotropy into account in order to obtain a smooth anisotropic sizing field for anisotropic mesh generation. Different types of anisotropic sources are described to represent boundary layers on surfaces and in volume that guarantee a smooth anisotropic field. This allows to us resolve multiple boundary layer intersections properly and naturally provides a smooth transition between the anisotropic boundary layer sizing and the isotropic region. Furthermore, the interaction between a smooth anisotropic sizing field and curvature is studied, and estimates of the tangential size spacing are provided for first and second order approximation of the geometry to ensure smoothness of the sizing field. It is also shown that, in order to get a smooth size variation, volumetric and surface meshing can not be decoupled. The filtering of the sources in order to obtain a computationally efficient method is described. Numerical examples demonstrate our method.