Sphericity: Mesh Optimization for Arbitrary Element Topology

In this paper, a new method for optimizing CFD meshes, based on the usage of a geometric quantity called Sphericity, is introduced. Sphericity is an element-wise property that provides a measure of the shapes deviation from a perfect sphere. When used as an objective in a gradient based framework, it results in a fast, scale invariant, optimization algorithm applicable to arbitrary finite volume element topologies. The methodology is heuristic in nature in that it does not consider known numerical quality metrics explicitly. Our study has however shown it to be exceptionally robust and effective in improving mesh quality, provided that grid topology does not introduce fundamentally concave cells. The main focus of this paper is the development of a robust optimization algorithm that can effectively handle complications arising from constraints imposed by surface interactions. Specifically, efficient heuristic and gradient based techniques, for handling difficult mesh topologies with acutely curved surfaces, feature edges and high aspect ratio layer cells are introduced. In combination with the base method, these measures ensure exceptional quality meshes even on industrial scale applications. As a final step, the method is integrated into a general purpose mesh motion framework, allowing the maintenance of high cell quality even during extreme deformation events. Examples and industrial applications in the context of adjoint based shape optimization are presented, illustrating the method’s general effectivenes