Keywords: mesh generation, hexahedral mesh, multi-sweeping, computational domain, geometry decomposition.

The generation of unstructured hexahedral meshes is still an open problem. Several methods have appeared in the literature to generate such meshes. However, an unstructured hexahedral mesher that can discretize any arbitrary geometry does not exist. Therefore, specific algorithms have been developed for specific types of geometries that often appear in industrial applications. For instance, sweep algorithms [1,2,3,4] have been successfully applied for extrusion geometries defined by a single source surface and a single target surface (one-to-one sweeping algorithms). This method evolved into the many-to-one algorithm [5] that allows meshing extrusion volumes with several source surfaces but a single target surface. The method decomposes the initial geometry into one-to-one barrels that can be meshed using a one-to-one sweeping scheme. In the last years, several algorithms have appeared to mesh many-to-many extrusion volumes (multi-sweeping algorithms) [6,7]. This algorithm decomposes the volume into many-to-one sub-volumes. Then, each sub-volume is further decomposed into one-to-one barrels. The decomposition is performed by means of projecting nodes along the sweep direction and imprinting surfaces.

However, the quality of the final mesh is directly related to the robustness of the imprinting process and to the location of inner nodes created during the decomposition process, especially for geometries with curved surfaces. To overcome these drawbacks, we propose two original contributions. On the one hand, we introduce the new concept of the computational domain for sweep geometries. The computational domain is a planar representation of the sweep levels and it permits improvement of several geometric calculations performed during the imprinting process. This results in a more robust imprinting process.

On the other hand, we propose to improve the location of inner nodes by performing a three-stage decomposition process. In the first stage, we project the nodes on target surfaces to source surfaces. At this stage, the decomposition of the geometry is determined, but it is desirable to improve the location of inner nodes. To this end, in the second stage, we project back the nodes from source surfaces to target surfaces. In the third stage, the final location of inner nodes is computed as a weighted average of the nodes projected from target surfaces and the nodes projected from source surfaces.

1

P. Knupp, "Next-generation sweep tool: a method for generating all-hex meshes on two-and-one-half dimensional geometries", in "Proceedings of the 7th International Meshing Roundtable", 1998.

2

M.L. Staten, S.A. Canann, S.J. Owen, "BMSweep: Locating interior nodes during sweeping"", Engineering with Computers, 15, 212-218, 1999. doi:10.1007/s003660050016

3

X. Roca, J. Sarrate, A. Huerta, "Mesh projection between parametric surfaces", Communications in Numerical Methods in Engineering, 22, 591-603, 2006. doi:10.1002/cnm.836

4

X. Roca, J. Sarrate, "An automatic and general least-squares projection procedure for sweep meshing", in "Proceedings of the 15th International Meshing Roundtable", 2006. doi:10.1007/978-3-540-34958-7_28

5

M.A. Scott, S.E. Benzley, S.J. Owen, "Improved many-to-one sweeping", International Journal for Numerical Methods in Engineering, 63, 332-348, 2006. doi:10.1002/nme.1444

6

T. Blacker, "The Cooper tool", in "Proceedings of the 5th International Meshing Roundtable", 1996.

7

D.R. White, S. Saigal, S. Owen, "CCSweep: an automatic decomposition multi-sweep volumes", Engineering with Computers, 20, 222-236, 2004. doi:10.1007/s00366-004-0290-6

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