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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.

MSC:
 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
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