Optimizing the geometrical accuracy of curvilinear meshes

TL;DR

This paper introduces a fast optimization method to improve the geometrical accuracy of high order curvilinear meshes, enhancing CFD solutions by reducing boundary inaccuracies and untangling invalid elements.

Contribution

A novel fast estimate of geometrical accuracy is used in an optimization process to improve high order mesh quality and validity.

Findings

Significant improvements in geometrical accuracy measured by Hausdorff distance.

Enhanced boundary smoothness benefits CFD solution accuracy.

Effective untangling of invalid high order mesh elements.

Abstract

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 Haudorff 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.