Entropy solution at concave corners and ridges, and volume boundary layer tangential adaptivity

• Published in: Journal of computational physics Vol. 376; pp. 1 - 19
• Main Authors: Aubry, R., Karamete, B.K., Mestreau, E.L., Jones, C., Dey, S.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.01.2019; Elsevier Science Ltd
• Subjects: Anisotropy; Boundary layer; Boundary layer transition; Computational physics; Concavity; Corners; Entropy; Entropy of solution; Mesh generation; Multiple normals; Numerical analysis; Ridges; Ridges and corners; Sizing; Tangential adaptivity; Volume mesh generation; Voronoi diagram; Voronoi graphs; Multiple normals; Volume mesh generation; Voronoi diagram; Tangential adaptivity; Ridges and corners; Boundary layer
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2018.09.030

Two particular aspects of volume boundary layer mesh generation applied to non smooth geometries are considered in this work. First, the treatment of concave ridges and corners is tackled from a generic viewpoint. Entropy satisfying elements are generated where shocks form in the volume. This proves useful to avoid premature halt of the boundary layer, and therefore potential jumps in the normal size. The connection with the Voronoi diagram is commented. Second, boundary layer adaptivity in the tangential plane is considered to honor arbitrary sizing prescription, and avoid size mismatch between the boundary layer and the isotropic sizing. It is shown that a strict semi-structured framework has to be abandoned in general to accommodate changes in the mesh topology. Size transition between boundary layer and fully unstructured anisotropic mesh is automatically taken into account. Both the concavity problem and the tangential adaptivity are presented together, since they require similar mesh operators. Various numerical examples illustrate the method. •We present a generic technique to adapt a semi-structured boundary layer mesh to an arbitrary sizing field.•We present a generic technique to deal with concave geometries within a semi-structured context.•We present how multiple normals interact with the previous items for arbitrary geometries with arbitrary sizing fields.