SUMMARYConformal refinement using a shrink and connect strategy, known as pillowing or buffer insertion, contracts and reconnects contiguous elements of an all-quadrilateral or an all-hexahedral mesh in order to locally increase vertex density without introducing hanging nodes or non-cubical elements. Using layers as shrink sets, the present method automates the anisotropic refinement of such meshes according to a prescribed size map expressed as a Riemannian metric field. An anisotropic smoother further enhances vertex clustering to capture the features of the metric. Both two-and three-dimensional test cases with analytic control metrics confirm the feasibility of the present approach and explore strategies to minimize the trade-off between element shape quality and size conformity. Additional examples using discrete metric maps illustrate possible practical applications. Although local vertex removal and reconnection capabilities have yet to be developed, the present refinement method is a step towards an automated tool for conformal adaptation of all-quadrilateral and all-hexahedral meshes.

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Summary. The proposed quad-dominant mesh adaptation algorithm is based on simplicial optimization. It is driven by an anisotropic Riemannian metric and uses specialized local operators formulated in terms of an L ∞ instead of the usual L2 distance. Furthermore, the physically-based vertex relocation operator includes an alignment force to explicitly minimize the angular deviation of selected edges from the local eigenvectors of the target metric. Sets of contiguous edges can then be effectively interpreted as active tensor lines. Those lines are not only packed but also simultaneous networked together to form a layered rectangular simplicial mesh that requires little postprocessing to form a cubical-dominant one. Almost all-cubical meshes are possible if the target metric is compatible with such a decomposition and, although presently only two-dimensional tests were performed, a three-dimensional extension is feasible.

The present paper describes an unstructured hexahedral mesh generator for viscous flow simulations around complex 3D configurations. The first step of this method is the geometric adaptation of an initial non-body-fitted mesh by grid embedding. The resulting octree mesh is then fitted to the actual boundaries of the domain and its main features, such as sharp edges and corners, are captured. Degenerated cells resulting from body-fitting are removed using a splitting strategy and by insertion of buffer layers. Finally, in vicinity of solid walls, layers of highly stretched cells are marched directly from the quadrilateral surface mesh that is a by-product of the body-fitting process. Interfacing between the layer and octree meshes only requires the deformation of the octree to insert the layers. The resulting method is highly automated and significantly reduces turnaround times. To illustrate its capabilities, both internal and external applications are presented.

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