An Entropy Satisfying Boundary Layer Surface Mesh Generation

Aubry, Romain; Dey, Saikat; Mestreau, Eric; Karamete, Kaan; Gayman, D.

doi:10.1137/140963625

Cited by 8 publications

(6 citation statements)

References 25 publications

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“…In this section, the multiple normal approach is recalled to prepare for the new algorithm presented in Section 4. Multiple normals are reminiscent of the gradient of the distance field close to a convex vertex, discretizing Huyghens principle , while also in practice enhancing visibility. In a semistructured context, a normal is associated with only one vertex.…”

Section: The Generic Multiple Normal Proceduresmentioning

confidence: 99%

“…In this section, the spherical Voronoi diagram is briefly recalled because it will dispense the main tool on which the new algorithm presented in Section 4 relies. As noted in , the boundary layer mesh generation can be recast as an offset of the surface mesh augmented with a mapping between both meshes. It appears clearly that distance, through the Eikonal equation, plays a fundamental role.…”

Section: The Spherical Voronoi Diagrammentioning

confidence: 99%

“…Normal vectors are closely related to distance field propagation through the Eikonal equation . Multiple normals are a consequence of expansion waves forming around ridges and corners . The main aim of the boundary layer generation may be recast as trying to reproduce a standard CAD offsetting, while providing a mapping between the discrete layers of the surface mesh.…”

Section: Introductionmentioning

confidence: 99%

“…The present work is an extension to three dimensions of . Based on the authors' investigations, four main capabilities were identified in these articles to be able to generate optimal smooth boundary layer on arbitrary geometries: Smooth anisotropic sizing field Multiple normals at corners and ridges Treatment of concavities in order to avoid premature halts Adaptivity in the tangent plane for thick boundary layers, because the size in the volume is very different from the size on the surface …”

Section: Introductionmentioning

confidence: 99%

“…The generation of smooth anisotropic sizing fields was discussed in , and carries automatically to volume generation, because the size specification was illustrated on surfaces but performed in the three‐dimensional space. The next three items were conducted in at once for the surface case. Concavities were treated on the surface by degenerating quads to triangles in the boundary layer.…”

Section: Introductionmentioning

confidence: 99%

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Boundary layer mesh generation on arbitrary geometries

Aubry

Dey

Mestreau

et al. 2017

Numerical Meth Engineering

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Volume boundary layer mesh generation on non-smooth geometries with multiple normals is considered in this work. A new highlight is given to corner and ridge boundary layer mesh generation through the generalized Voronoi diagram in general, and the spherical Voronoi diagram in particular. This provides the keystone to allow for the first time boundary layer mesh generation at arbitrary corner configurations. The work proposed in [18] is revisited and compared with the new approach. A detailed description of the new algorithm is provided. The spherical Voronoi diagram delivers geometrically the optimal normals as well as topologically the optimal connectivities, as far as normality is concerned. Numerical examples illustrate the accuracy and robustness of the method. This approach seems to handle arbitrary geometry boundary layer mesh generation, in theory as well as in practice.This example represents a cube inside another cube and is illustrated in Figure 5. Some archetypal convex corners are displayed. The difficulty here relies in accurately meshing the mixed convex concave corners. Because of the planar faces, it is easier to appreciate the exact position of the extruded surface. The intersection between the convex ridges and the planar faces are exact, thanks to the location of the Voronoi bisectors for the direction, and the geodesic distance for the computation of the offset modulus. The spherical Voronoi diagram for each of these mixed corners corresponds to the one presented before in Figure 3. The relevant part consists of the spherical parabolic bisectors between the reflex vertex and the bottom face. As mentioned in Section 4, because of the particular surface discretization, this bisector has been split in various parts. Algorithm 3 gathers all these bisectors to create only one group. The group is then meshed along its bisector given the angle provided for discretizing the multiple normals. This group is a vertex/edge bisector. Then, Algorithm 4 sew these edges with the multiple normals from the ridge on one side, and to the triangle faces associated with the bisectors on the other side. The final mesh has 23 Kpoints and 125 Kelems. The boundary layer has 10 layers and reaches up to layer 5 before producing inverted elements. Sharov exampleThis example is extracted from [12] and is displayed in Figure 6. Four ridges abut on the complex corner, two concave and two convex. There is no single normal that ensures visibility for the complex corner of this geometry. Therefore, multiple normals are mandatory for this example. The Voronoi diagram is quite complex for this example, and presents two reflex vertices arising from the two convex ridges. It displays the geometry vertex/edge bisectors and the vertex/vertex bisectors. For this example, Algorithm 3 identifies three different groups, one for the vertex/vertex bisector and two BOUNDARY LAYER MESH GENERATION ON ARBITRARY GEOMETRIES 167 Figure 5. A cube inside a cube.for the edge/vertex bisectors associated with the two different reflex vertices. The zo...

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Section: The Generic Multiple Normal Proceduresmentioning

confidence: 99%

Section: The Spherical Voronoi Diagrammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%