Boundary Representation Tolerance Impacts on Mesh Generation and Adaptation

P3 Bézier CAD Surrogates for anisotropic mesh adaptation

“…Concretely, this means that there can actually be gaps between faces meant to share an edge, or that neighbouring faces may be interpenetrating at scales that cannot be neglected by the meshing algorithm. The paper [16] goes over this issue in great detail, illustrating the impact on mesh adaptation for CFD problems. For instance, it is frequent for wing and fuselage intersections to be given with a tolerance several orders of magnitude higher than the smallest prescribed mesh size in this area by the end of adaptation.…”

“…Furthermore, derivatives of the parameterizations are used to compute metric fields for surface error approximation [18,19] or surface normals and tangent planes. Once more, the CAD description may pose problems such as by having faces map portions of edges onto points (degeneracy) or having unwanted local features such as folds under the tolerance (another issue pointed out in [16]). In particular, derivatives are not defined at these points and unstable in their vicinity.…”

“…For this reason, it is not infrequent for CAD models to pose a number of di culties, such as by not being watertight, having face lines that degenerate into single points, autointersecting faces, interpenetrating neighbouring faces, illconditioned parameterizations, unintended small features, etc... [14,15] go over the reasons for these features in detail. Furthermore, these errors are often bound by tolerances too high for the purposes of mesh adaptation where smaller edges may be required close to or on the surface [16]. Strategies to combat these issues operate at essentially two levels: by correcting the CAD before it is used in meshing, and by devising robust tessellation algorithms.…”