Optimizing the geometrical accuracy of curvilinear meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:310

Article

Toulorge, Thomas^1,3  Lambrechts, Jonathan^2,3  Remacle, Jean-Francois² 

[1] PSL Res Univ, MINES ParisTech, CEMEF, CNRS UMR 7635, 1 Rue Claude Daunesse,CS 10207, F-06904 Sophia Antipolis, France

[2] Catholic Univ Louvain, Inst Mech Mat & Civil Engn iMMC, Batiment Euler,Ave Georges Lemaitre 4, B-1348 Louvain La Neuve, Belgium

[3] Fonds Natl Rech Sci, Rue Egmond 5, B-1000 Brussels, Belgium

关键词: High order mesh;    Geometrical accuracy;    Hausdorff distance;   

DOI  :  10.1016/j.jcp.2016.01.023

来源: Elsevier

【 摘 要 】

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Hausdorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a particular role of the enhanced mesh boundary smoothness. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free