Variational generation of prismatic boundary-layer meshes for biomedical computing.

*(English)*Zbl 1171.76440Summary: Boundary-layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary-layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary-layer meshes for such complex geometries. Our method computes a feature size of the geometry, adapts the surface mesh based on the feature size, and then generates the prismatic layers by propagating the triangulated surface using the face-offsetting method. We derive a new variational method to optimize the prismatic layers to improve the triangle shapes and edge orthogonality of the prismatic elements and also introduce simple and effective measures to guarantee the validity of the mesh. Coupled with a high-quality tetrahedral mesh generator for the interior of the domain, our method generates high-quality hybrid meshes for accurate and efficient numerical simulations. We present comparative study to demonstrate the robustness and quality of our method for complex biomedical geometries.

##### MSC:

76M30 | Variational methods applied to problems in fluid mechanics |

76Z05 | Physiological flows |

92-08 | Computational methods for problems pertaining to biology |

65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |

65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |

##### Keywords:

mesh generation; prismatic boundary layers; gradient-limited feature size; face offsetting; variational optimization
PDF
BibTeX
XML
Cite

\textit{V. Dyedov} et al., Int. J. Numer. Methods Eng. 79, No. 8, 907--945 (2009; Zbl 1171.76440)

Full Text:
DOI

##### References:

[1] | Kadirvel, The influence of hemodynamic forces on biomarkers in the walls of elastase-induced aneurysms in rabbits, Neuroradiology 49 (1) pp 1041– (2007) |

[2] | Schirmer, Wall shear stress gradient analysis within an idealized stenosis using non-Newtonian flow, Neurosurgery 61 pp 853– (2007) |

[3] | De Backer, Computational fluid dynamics can detect changes in airway resistance in asthmatics after acute bronchodilation, Journal of Biomechanics 41 pp 106– (2007) |

[4] | Kleinstreuer, Computational analyses of a pressurized metered dose inhaler and a new drug-aerosol targeting methodology, Journal of Aerosol Medicine 20 (3) pp 294– (2007) |

[5] | Lorensen WE, Cline HE. Marching cubes: a high resolution 3d surface construction algorithm. Proceedings of the SIGGRAPH 87, vol. 21, 1987; 163-169. |

[6] | Treece, Regularised marching tetrahedra: improved iso-surface extraction, Computers and Graphics 23 (4) pp 583– (1999) |

[7] | Nielson, On marching cubes, IEEE Transactions on Visualization and Computer Graphics 9 (3) pp 283– (2003) |

[8] | Newman, A survey of the marching cubes algorithm, Computers and Graphics 30 pp 854– (2006) |

[9] | Miao, Effects of flow patterns on the localization and expression of VE-Cadherin at vascular endothelial cell junctions: in vivo and in vitro investigations, Journal of Vascular Research 42 (1) pp 77– (2005) |

[10] | Giannoglou, Wall pressure gradient in normal left coronary artery tree, Medical Engineering and Physics 27 (6) pp 455– (2005) |

[11] | Chien, Molecular basis of mechanical modulation of endothelial cell migration, Frontiers in Bioscience 10 pp 1985– (2005) |

[12] | Zarins, Finite element modeling of blood flow in arteries, Computer Methods in Applied Mechanics and Engineering 158 pp 155– (1998) · Zbl 0953.76058 |

[13] | Longest, Comparison of blood particle deposition models for non-parallel flow domains, Journal of Biomechanics 36 (3) pp 421– (2003) |

[14] | Chiou, Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder, Acta Mechanica 129 pp 1619– (1998) · Zbl 0929.76138 |

[15] | Kroger, Particle deposition in a turbulent boundary layer over a large particle size spectrum, Journal of Aerosol Science 28 pp 631– (1997) |

[16] | Kuprat, An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data, Journal of Computational Physics 228 (3) pp 619– (2009) · Zbl 1158.65016 · doi:10.1016/j.jcp.2008.09.030 |

[17] | Jiao, Face offsetting: A unified approach for explicit moving interfaces, Journal of Computational Physics 220 pp 612– (2007) · Zbl 1109.65020 |

[18] | ThompsonJF, SoniBK (eds). Handbook of Grid Generation. CRC Press: Boca Raton, 1999. · Zbl 0980.65500 |

[19] | Kallinderis, Prismatic grid generation for three-dimensional complex geometries, AIAA Journal 31 pp 1850– (1993) · Zbl 0798.76075 |

[20] | Pirzadeh, Unstructured viscous grid generation by advancing-layers method, AIAA Journal 32 pp 1735– (1994) · Zbl 0900.76487 |

[21] | Khawaja A, McMorris H, Kallinderis Y. Hybrid grids for viscous flows around complex 3-d geometries including multiple bodies. AIAA-95-1685, 1995. · Zbl 0900.76488 |

[22] | Pirzadeh, Three-dimensional unstructured viscous grids by the advancing-layers methods, AIAA Journal 34 pp 43– (1996) · Zbl 0900.76487 |

[23] | Hassan, Unstructured tetrahedral mesh generation for three-dimensional viscous flows, International Journal for Numerical Methods in Engineering 39 pp 549– (1996) · Zbl 0844.76051 |

[24] | Garimella, Boundary layer mesh generation for viscous flow simulations, International Journal for Numerical Methods in Engineering 49 pp 193– (2000) · Zbl 0960.76074 |

[25] | Ito, Improvements in the reliability and quality of unstructured hybrid mesh generation, International Journal for Numerical Methods in Fluids 45 pp 79– (2004) · Zbl 1072.76054 |

[26] | Athanasiadis, A folding/unfolding algorithm for the construction of semi-structured layers in hybrid grid generation, Computer Methods in Applied Mechanics and Engineering 194 pp 5051– (2005) · Zbl 1094.76050 |

[27] | Wang, Proceedings of the 15th International Meshing Roundtable (2006) |

[28] | Ito, Multiple marching direction approach to generate high quality hybrid meshes, AIAA Journal 45 pp 162– (2007) |

[29] | Aubry, Generation of viscous grids at ridges and corners, International Journal for Numerical Methods in Engineering 77 (9) pp 1247– (2008) · Zbl 1156.76432 · doi:10.1002/nme.2446 |

[30] | Sharov, Hybrid prismatic/tetrahedral grid generation for viscous flow applications, AIAA Journal 36 pp 157– (1998) · Zbl 0908.76080 |

[31] | LĂ¶hner, Generation of non-isotropic unstructured grids via directional enrichment, International Journal for Numerical Methods in Engineering 49 pp 219– (2000) · Zbl 0970.76058 |

[32] | Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (1999) · Zbl 0973.76003 |

[33] | Sethian, Curvature flow and entropy conditions applied to grid generation, Journal of Computational Physics 115 pp 440– (1994) · Zbl 0837.65134 |

[34] | Wang, Eikonal equation-based front propagation for arbitrary complex configurations, International Journal for Numerical Methods in Engineering 73 pp 226– (2008) · Zbl 1167.74051 |

[35] | Edelsbrunner, Geometry and topology for mesh generation, Discrete and Computational Geometry (2001) · Zbl 0981.65028 |

[36] | Cormen, Introduction to Algorithms (2001) |

[37] | Smits B. Efficiency issues for ray tracing. ACM SIGGRAPH 2005 Courses, 2005; 6. Available from: http://doi.acm.org/10.1145/1198555.1198745. |

[38] | Khamayseh, Use of the spatial kd-tree in computational physics applications, Communications in Computational Physics 2 pp 545– (2007) · Zbl 1164.65319 |

[39] | Jiao X, Zha H. Consistent computation of first- and second-order differential quantities for surface meshes. ACM Solid and Physical Modeling Symposium, Stony Brook, New York, U.S.A., 2008; 159-170. |

[40] | Jiao X, Wang D, Zha H. Simple and effective variational optimization of surface and volume triangulations. Proceedings of the 17th International Meshing Roundtable 2008; to appear. |

[41] | Heath, Scientific Computing: An Introductory Survey (2002) |

[42] | Si, Adaptive tetrahedral mesh generation by constrained Delaunay refinement, International Journal for Numerical Methods in Engineering (2008) · Zbl 1195.65129 |

[43] | Shewchuk, General-dimensional constrained Delaunay and constrained regular triangulations. I: combinatorial properties, Discrete and Computational Geometry 39 pp 580– (2008) · Zbl 1142.52010 |

[44] | Amenta, Surface reconstruction by Voronoi filtering, Discrete and Computing Geometry 22 pp 481– (1999) · Zbl 0939.68138 |

[45] | Amenta N, Bern M, Kamvysselis M. A new Voronoi-based surface reconstruction algorithm. Proceedings of the SIGGRAPH 98, Orlando, FL, U.S.A., 1998; 415-421. |

[46] | Dheeravongkit, Inverse adaptation of a hex-dominant mesh for large deformation finite element analysis, Computer Aided Design 39 pp 427– (2007) · Zbl 1160.68620 |

[47] | Knupp, Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II-a framework for volume mesh optimization and the condition number of the Jacobian matrix, International Journal for Numerical Methods in Engineering 48 pp 1165– (2000) · Zbl 0990.74069 |

[48] | Zhang Y, Bajaj C. Finite element meshing for cardiac analysis. Technical Report 04-26, The University of Texas at Austin, 2004. |

[49] | Zhang, 3d finite element meshing from imaging data, Computer Methods in Applied Mechanics in Engineering 194 pp 5083– (2005) · Zbl 1093.65019 |

[50] | Rivara, New longest-edge algorithms for the refinement and/or improvement of unstructured triangulations, International Journal for Numerical Methods in Engineering 40 pp 3313– (1997) · Zbl 0980.65144 |

[51] | Kuprat, Volume conserving smoothing for piecewise linear curves, surfaces, and triple lines, Journal of Computational Physics 172 pp 99– (2001) · Zbl 0988.65010 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.