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Optimizing the geometrical accuracy of 2D curvilinear meshes

Remacle, Jean-Francois and Jonathan Lambrechts, Christophe Geuzaine, Thomas Toulorge

23rd International Meshing Roundtable, Elsevier Ltd., October 12-15 2014

IMR
PROCEEDINGS

23rd International Meshing Roundtable
London, UK
October 12-15,2014

Universite catholique de Louvain, Institute of Mechanics, Belgium
Universite de Liege, Belgium
Fonds National de la Recherche Scientifique, Belgium
Email: jean-francois.remacle@uclouvain.be

Summary
This paper presents a method to generate valid 2D high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a straight sided mesh. High order points are initially snapped to the real geometry without taking care of the validity of the high order elements. An optimization procedure that both allow to untangle invalid elements and to optimize the geometrical accuracy of the mesh is presented. An area based distance is proposed to compute the geometrical discrepancy between the mesh and its underlying geometry. This area based distance is shown to be strongly related to standard distance measures such as the Hausdor distance, while being largely faster to compute. The new distance is minimized through an unconstrained optimization procedure, allowing significant improvements of the geometrical accuracy of high order meshes. A simple computational example shows that geometrically optimized meshes allow smooth CFD solutions.

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