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Eikonal equation‐based front propagation for arbitrary complex configurations
Author(s) -
Wang Y.,
Guibault F.,
Camarero R.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2063
Subject(s) - eikonal equation , tangent , classification of discontinuities , offset (computer science) , geometry , regular polygon , cartesian coordinate system , wedge (geometry) , mathematics , front (military) , mathematical analysis , engineering , computer science , mechanical engineering , programming language
This paper presents a front propagation method using the Eikonal equation, ∇ϕ ⋅ ∇ϕ = 1, in which, ϕ represents the smallest Euclidean distance field to the front to be propagated. The offset capturing approach consists in first calculating the ϕ field over a uniform Cartesian grid fully covering the front to be propagated, and then constructing the iso‐ϕ curves or surfaces as the propagated result. The calculation of ϕ 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 propagated and demonstrated 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. Copyright © 2007 John Wiley & Sons, Ltd.