Connectivity-change moving mesh methods for high-order meshes: Toward closed advancing-layer high-order boundary layer mesh generation

Abstract

To cite this version:Rémi Feuillet, Adrien Loseille, David Marcum, Frédéric Alauzet. Connectivity-change moving mesh methods for high-order meshes: Toward closed advancing-layer high-order boundary layer mesh generation.Curved mesh generation starting from a P 1 mesh and closed advancing-layer boundary layer mesh generation both rely on mesh deformation and mesh optimization techniques. The approach presented in this work is to generalize connectivity-change moving mesh methods to high-order meshes. This approach is based on a high-order linear elasticity solver for the mesh deformation and on high-order mesh optimization operators such as mesh smoothing and generalized swapping. Thanks to this method, P k meshes are generated from P 1 meshes and closed advancing-layer boundary layer mesh generation will soon be possible.

P3 Bézier CAD Surrogates for anisotropic mesh adaptation

“…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]).…”

“…A constrained Delaunay mesher in parametric domain D is then called with this boundary as input. This first tessellation is used to compute the surface approximation error metric in low [18] or in high order [19]. When constructing the P 1 mesh as support for the P 3 surface mesh, a P 3 geometric approximation metric is used to adapt the surface mesh.…”

Efficient exascale discretizations: High-order finite element methods

“…In particular, methods are needed to effectively support the definition of well shaped elements in the application of ALE methods in Lagrangian reference frame simulations when meshes become highly deformed, or in the application of cavity based curved mesh modifications where new curved mesh entities must be defined within a curved mesh cavity. Methods that apply direct curved element shape optimization are being used to address these needs (Dobrev et al, 2019; Feuillet et al, 2018).…”

Efficient Exascale Discretizations: High-Order Finite Element Methods

“…In particular, methods are needed to effectively support the definition of well shaped elements in the application of ALE methods in Lagrangian reference frame simulations when meshes become highly deformed, or in the application of cavity based curved mesh modifications where new curved mesh entities must be defined within a curved mesh cavity. Methods that apply direct curved element shape optimization are being used to address these needs (Dobrev et al 2019;Feuillet et al 2018). The MFEM, libCEED, NekRS, and libParanumal software packages developed as part of the CEED project all include support for performance portability achieved to varying degrees using the Open Concurrent Compute Abstraction (OCCA) (Medina et al 2014;OCCA).…”