Algorithmic Improvements to Sweeping and Multi-Sweeping Volume Mesh Generation.

摘要

Due to numerical properties, hexahedral meshes are preferred and widely used for numerical simulations in several engineering domains. One of the most robust and widely used algorithms for all-hexahedral meshes is the sweeping algorithm which can generate the hexahedral meshes by sweeping the surface meshes on the source surfaces to the target surfaces. In addition, sweeping is also useful for generating other swept volume meshes besides hexahedral meshes such as tri-prism for alignment. The sweeping algorithm consists of four main steps: surface mesh generation on the source surfaces, projection of source surface meshes onto the target surfaces, structured mesh generation on the linking surfaces and interior node placement inside volumes. Current state of the art suffers from either low robustness or poor mesh quality: surface mesh mapping between concave or multiply-connected domains with inverted elements, poor interior node placement inside volumes with complicated internal structures, poor imprinting algorithm for multi-sweeping problems and failed corner assignment for vertices with ambiguous angles on the linking surfaces. Therefore, in this work, an improved and robust sweeping tool has been developed, which consists of several things: surface mesh mapping between the s/t surfaces has been developed based on Harmonic Mapping which works for convex, concave and multiply-connected surfaces; interior node placement method inside volumes has been developed based on the Cage-based Morphing which can deal with local deformation from the linking surfaces and relocate interior nodes accordingly; an improved imprinting algorithm for multi-sweeping has been developed where edge patches are imprinted between the source and target surfaces; an optimal corner assignment method on the linking surfaces has been developed based on templates and LP. Finally, the sweepability assessment problems are discussed based on the topological constraints, geometric constraints and some constraints from users' specified matchings. Overall, our improved sweeping algorithm can generate a swept volume mesh with good mesh quality and O(nlogn) time complexity.