Abstract
Converting a hex mesh into a fundamental mesh by inserting fundamental sheets is an effective means to improve the hex mesh’s quality near the boundary. However, the high-quality and automatic fundamental sheets insertion is still a problem. In this paper, a method is proposed to automatically generate fundamental sheets with the support of stream surfaces. By establishing a constrained integer linear system, the types of fundamental sheets to be inserted are determined effectively and optimally. By constructing discrete stream surfaces associated with the relevant geometric entities, the optimized positions of fundamental sheets are automatically determined. The experimental results show that the proposed method can automatically insert high-quality fundamental sheets and effectively improve the elements’ geometric quality of the hex mesh.
Issue Section:
Research Papers
References
1.
Blacker
, T. D.
, 2001
, “Automated Conformal Hexahedral Meshing Constraints, Challenges and Opportunities
,” Eng. Comput.
, 17
(3
), pp. 201
–210
. 10.1007/PL000133842.
Cook
, W. A.
, and Oaks
, W. R.
, 1982
, “Mapping Methods for Generating Three-Dimensional Meshes
,” Comp. Mech. Eng.
, 1
(1
), pp. 67
–72
.3.
Ruiz-Gironés
, E.
, and Sarrate
, J.
, 2010
, “Generation of Structured Meshes in Multiply Connected Surfaces Using Submapping
,” Adv. Eng. Software
, 41
(2
), pp. 379
–387
. 10.1016/j.advengsoft.2009.06.0094.
Staten
, M. L.
, Kerr
, R. A.
, Owen
, S. J.
, Blacker
, T. D.
, Stupazzini
, M.
, and Shimada
, K.
, 2010
, “Unconstrained Plastering—Hexahedral Mesh Generation via Advancing-Front Geometry Decomposition
,” Int. J. Numer. Methods Eng.
, 81
(2
), pp. 135
–171
. 10.1002/nme.26795.
Tautges
, T. J.
, Blacker
, T.
, and Mitchell
, S. A.
, 1996
, “The Whisker Weaving Algorithm: A Connectivity-Based Method for Constructing all-Hexahedral Finite Element Meshes
,” Int. J. Numer. Methods Eng.
, 39
(19
), pp. 3327
–3349
. 10.1002/(SICI)1097-0207(19961015)39:19<3327::AID-NME2>3.0.CO;2-H6.
Schneiders
, R.
, and Bunten
, R.
, 1995
, “Automatic Generation of Hexahedral Finite Element Meshes
,” Comput. -Aided Geom. Des.
, 12
(7
), pp. 693
–707
. 10.1016/0167-8396(95)00013-V7.
Owen
, S. J.
, Shih
, R. M.
, and Ernst
, C.
, 2017
, “A Template-Based Approach for Parallel Hexahedral two-Refinement
,” Comput.-Aided Des.
, 85
(SI
), pp. 34
–52
. 10.1016/j.cad.2016.09.0058.
Lu
, Y.
, Gadh
, R.
, and Tautges
, T. J.
, 2001
, “Feature Based Hex Meshing Methodology: Feature Recognition and Volume Decomposition
,” Comput.-Aided Des.
, 33
(3
), pp. 221
–232
. 10.1016/S0010-4485(00)00122-69.
Wu
, H.
, Gao
, S.
, Wang
, R.
, and Chen
, J.
, 2018
, “Fuzzy Clustering Based Pseudo-Swept Volume Decomposition for Hexahedral Meshing
,” Comput.-Aided Des.
, 96
, pp. 42
–58
. 10.1016/j.cad.2017.10.00110.
He
, Y.
, Wang
, H.
, Fu
, C.
, and Qin
, H.
, 2009
, “A Divide-and-Conquer Approach for Automatic Polycube map Construction
,” Comput. Graphics
, 33
(3
), pp. 369
–380
. 10.1016/j.cag.2009.03.02411.
Huang
, J.
, Jiang
, T.
, Shi
, Z.
, Tong
, Y.
, Bao
, H.
, and Desbrun
, M.
, 2014
, “l1-based Construction of Polycube Maps From Complex Shapes
,” ACM Trans. Graphics
, 33
(3
), pp. 25:1
–11
. 10.1145/260214112.
Nieser
, M.
, Reitebuch
, U.
, and Polthier
, K.
, 2011
, “CubeCover–Parameterization of 3D Volumes
,” Comput. Graphics Forum
, 30
(5
), pp. 1397
–1406
. 10.1111/j.1467-8659.2011.02014.x13.
Li
, Y.
, Liu
, Y.
, Xu
, W.
, Wang
, W.
, and Guo
, B.
, 2012
, “All-Hex Meshing Using Singularity-Restricted Field
,” ACM Trans. Graphics
, 31
(6
), pp. 177:1
–11
. 10.1145/2366145.236619614.
Jiang
, T.
, Huang
, J.
, Wang
, Y.
, Tong
, Y.
, and Bao
, H.
, 2014
, “Frame Field Singularity Correction for Automatic Hexahedralization
,” IEEE Trans. Visualization Comput. Graphics
, 20
(8
), pp. 1189
–1199
. 10.1109/TVCG.2013.25015.
Liu
, H.
, Zhang
, P.
, Chien
, E.
, Solomon
, J.
, and Bommes
, D.
, 2018
, “Singularity-constrained Octahedral Fields for Hexahedral Meshing
,” ACM Trans. Graphics
, 37
(4
), pp. 93:1
–17
. 10.1145/3197517.320134416.
Blacker
, T.
, Mitchell
, S. A.
, Tautges
, T. J.
, Murdoch
, P.
, and Benzley
, S.
, 1997
, “Forming and Resolving Wedges in the Spatial Twist Continuum
,” Eng. Comput.
, 13
(1
), pp. 35
–47
. 10.1007/BF0120185917.
Hecht
, F.
, Kuate
, R.
, and Tautges
, T.
, 2012
, “Local Transformations of Hexahedral Meshes of Lower Valence
,” Comput. Geom. Theory Appl.
, 45
(1
), pp. 62
–71
. 10.1016/j.comgeo.2011.07.00218.
Wang
, R.
, Gao
, S.
, Zheng
, Z.
, and Chen
, J.
, 2018
, “Hex Mesh Topological Improvement Based on Frame Field and Sheet Adjustment
,” Comput.-Aided Des.
, 103
(SI
), pp. 103
–117
. 10.1016/j.cad.2017.11.00719.
Shepherd
, J. F.
, 2009
, “Conforming Hexahedral Mesh Generation via Geometric Capture Methods
,” Proceedings of the 18th International Meshing Roundtable
, Salt Lake City, UT
, Oct. 25–28
, Heidelberg, Springer, pp. 85
–102
.20.
Jain
, R.
, and Tautges
, T. J.
, 2013
, “PostBL: Post-Mesh Boundary Layer Mesh Generation Tool
,” Proceedings of the 22nd International Meshing Roundtable
, Orlando, FL
, Oct. 13–16
, Cham, Springer, pp. 331
–348
.21.
Ledoux
, F.
, Goff
, L. N.
, Owen
, S. J.
, Staten
, M. L.
, and Weill
, J. C.
, 2012
, “A Constraint-Based System to Ensure the Preservation of Sharp Geometric Features in Hexahedral Meshes
,” Proceedings of the 21st International Meshing Roundtable
, San Jose, CA
, Oct. 7–10
, Heidelberg, Springer, pp. 315
–332
.22.
Wang
, R.
, Shen
, C.
, Chen
, J.
, Wu
, H.
, and Gao
, S.
, 2017
, “Sheet Operation Based Block Decomposition of Solid Models for Hex Meshing
,” Comput.-Aided Des.
, 85
(SI
), pp. 123
–137
. 10.1016/j.cad.2016.07.01623.
Wang
, R.
, Ding
, M.
, Wu
, H.
, Zheng
, Z.
, and Gao
, S.
, 2020
, “Optimization Design Method of Complex Sheet Insertion Operation of Hexahedral Mesh
,” J. Comput.-Aided Des. Comput. Graphics
, 32
(5
), pp. 846
–856
.24.
Carey
, G. F.
, 2002
, “Hexing the tet
,” Commun. Numer. Meth. Eng.
, 18
(3
), pp. 223
–227
. 10.1002/cnm.48525.
Chen
, J.
, Gao
, S.
, Wang
, R.
, and Wu
, H.
, 2016
, “An Approach to Achieving Optimized Complex Sheet Inflation Under Constraints
,” Comput. Graphics
, 59
(SI
), pp. 39
–56
. 10.1016/j.cag.2016.05.001Copyright © 2020 by ASME
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