Optimizing the geometrical accuracy of curvilinear meshes
For computational scientists using high-order methods, this provides a practical optimization to improve mesh accuracy and solution quality, though it is an incremental improvement over existing mesh optimization techniques.
This paper introduces a fast estimate of geometrical accuracy for high-order curvilinear meshes based on Taylor expansions, enabling an optimization procedure that significantly improves mesh accuracy as measured by Hausdorff distance, with demonstrated benefits for CFD solutions.
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.