zbMATH — the first resource for mathematics

Eikonal equation-based front propagation for arbitrary complex configurations. (English) Zbl 1167.74051
Summary: This paper presents a front propagation method using the eikonal equation, \(\nabla \phi \cdot \nabla \phi =1 \), in which, \(\phi\) represents the smallest Euclidean distance field to the front to be propagated. The offset capturing approach consists in first calculating the \(\phi\) field over a uniform Cartesian grid fully covering the front to be propagated, and then constructing the iso-\(\phi\) curves or surfaces as the propagated result. The calculation of \(\phi\) uses a 3D numerical scheme, the fast sweeping scheme. Validation for accuracy of the method is presented using academic test cases. A real 3D industry application, draft tube with two piers, is successfully solved using special boundary conditions to cope with inlet and outlet planes during front propagtion. This application involves the propagation of a front that exhibits both concave and convex shape regions, sharp corners, and local tangent plane surface discontinuities as well as a multi-connected domain.

74S30 Other numerical methods in solid mechanics (MSC2010)
76M25 Other numerical methods (fluid mechanics) (MSC2010)
74S20 Finite difference methods applied to problems in solid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
Full Text: DOI
[1] Unstructured viscous grid generation by advancing-layers method. AIAA 11th Applied Aerodynamics Conference, no. AIAA-93-3453, Monterey, CA, August 1993; 420–434.
[2] Un mailleur hybride structuré/non structuré en trois dimensions. Ph.D. Thesis, École Polytechnique de Montréal, 1998.
[3] Smereka, Annual Review of Fluid Mechanics 35 pp 341– (2003)
[4] Park, Computer-Aided Design 35 pp 501– (2003)
[5] Lee, Computer-Aided Design 35 pp 511– (2003)
[6] Malladi, IEEE International Conference on Image Processing 1 pp 489– (1996) · doi:10.1109/ICIP.1996.559540
[7] Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer: New York, 2003. · Zbl 1027.68137
[8] Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press: Cambridge, 1999. · Zbl 0973.76003
[9] Boue, SIAM Journal on Numerical Analysis 36 pp 667– (1999)
[10] Zhao, Mathematics of Computation 74 pp 603– (2005)
[11] Suillivan, Finite Elements in Analysis and Design 25 pp 275– (1997)
[12] Glimm, SIAM Journal on Scientific Computing 21 pp 2240– (2000)
[13] B-spline curves, boeing document, class notes, b-7150-bb-wp-2811d-4412, 1981.
[14] Tiller, IEEE Computer Graphics and Applications 4 pp 36– (1984)
[15] Coquillart, Computer-Aided Design 19 pp 305– (1987)
[16] Kulczycka, Computer-Aided Design 34 pp 19– (2002)
[17] Piegl, Computer-Aided Design 31 pp 147– (1999) · Zbl 0672.65009
[18] Sun, Computer-Aided Design 36 pp 1161– (2004)
[19] Farouki, Computer-Aided Geometric Design 3 pp 15– (1986)
[20] Osher, Journal of Computational Physics 79 pp 12– (1988)
[21] Sethian, Proceedings of the National Academy of Sciences of the United States of America 93 pp 1591– (1996)
[22] Kimmel, Computer-Aided Design 25 pp 154– (1993)
[23] Sethian, Journal of Computational Physics 115 pp 440– (1994)
[24] Qian, SIAM Journal on Numerical Analysis 45 pp 83– (2007)
[25] Qian, Journal of Scientific Computing (2006)
[26] Rouy, SIAM Journal on Numerical Analysis 29 pp 867– (1992)
[27] Bonet, International Journal for Numerical Methods in Engineering 31 pp 1– (1991)
[28] , , . A parametrization transporting surface offset construction method based on the Eikonal equation. Seventeenth AIAA CFD Conference, Toronto, ON, Canada, June 2005.
[29] , . Automatic near-body domain decomposition using the Eikonal equation. Proceedings of the 14th International Meshing Roundtable, Sandia National Laboratory. Springer: Berlin, September 2005.
[30] . Hybrid mesh generation for viscous flow simulations. Proceedings of the 15th International Meshing Roundtable, Sandia National Laboratory. Springer: Berlin, September 2006.
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.