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We propose an a posteriori approach for generating curved meshes for viscous flow simulations composed by high-order tetrahedra. The proposed approach is performed in the following three steps: (1) generate a linear tetrahedral mesh for inviscid flow; (2) insert a boundary layer mesh, composed by linear tetrahedra, on the viscous part; and (3) convert the linear tetrahedral mesh to a curved and high-order mesh for viscous flow. This approach provides high-order tetrahedral meshes with boundary layer parts that are composed by elements that are: curved, valid, and of any interpolation degree.

A procedure to quantify the distortion (quality) of a high-order mesh composed by curved tetrahedral elements is presented. The proposed technique has two main applications. First, it can be used to check the validity and quality of a high-order tetrahedral mesh. Second, it allows the generation of curved meshes composed by valid and high-quality high-order tetrahedral elements. To this end, we describe a method to simultaneously smooth and untangle high-order tetrahedral meshes by minimizing the proposed mesh distortion. Finally, we present several results to illustrate the two main applications of the proposed technique.

The aim of this work is to develop a simultaneous smoothing-untangling procedure for parametrized surfaces. To this end we will extend the definition of the quality metrics for planar meshes to parametrized surface meshes. Then, we will develop a minimization approach on the parametric space that will allow smoothing and untangling the surface mesh. To this end, first we will increase the robustness of the standard untangling techniques. Then, we will focus on the improvement of the computational efficiency of the developed approach. Finally, several examples will be presented in order to illustrate the capabilities of the proposed method.. L'objectiu d'aquest projecte és la millora de la qualitat de malles d'elements finits generades sobre superficies paramètriques. Aquestes malles podran estar formades per triangles o quadrilàters. Aquesta millora es realitzarà mitjançant la minimització numèrica d'una mesura de la qualitat de la malla definida en l'espai paramètric

Barcelona Supercomputing Center In this work, two new methods are presented: first, a given linear tetrahedral volume mesh is refined in such a way that its boundary tends to an almost everywhere C^2-continuous surface, and second, a curved high-order tetrahedral mesh which boundary approximates an almost everywhere C^2 surface is generated from a linear tetrahedral mesh. The aim of these curved meshes is to provide an almost everywhere C^2 smooth parametrization of curved boundaries suitable for finite element analysis with unstructured high-order methods. To illustrate the applicability of the methods, several curved high-order volume meshes have been generated from linear meshes obtained by digitizing real volumes.

Barcelona Supercomputing Center

Barcelona Supercomputing Center In this work, two new methods are presented: first, a given linear tetrahedral volume mesh is refined in such a way that its boundary tends to an almost everywhere C^2-continuous surface, and second, a curved high-order tetrahedral mesh which boundary approximates an almost everywhere C^2 surface is generated from a linear tetrahedral mesh. The aim of these curved meshes is to provide an almost everywhere C^2 smooth parametrization of curved boundaries suitable for finite element analysis with unstructured high-order methods. To illustrate the applicability of the methods, several curved high-order volume meshes have been generated from linear meshes obtained by digitizing real volumes.