Eikonal Equation Based Front Propagation Technique and its Applications
Yuanli Wang · 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition · 2009
This paper presents a new front propagation technique which is extended to the applications in Ge-ometryModeling andMeshGeneration. The propagation process proposed in this technique is directly inspired from marching technology, that is all the points located on the original front are propagated along their local normal directions. The main difference between the current method and traditional marching methods lies in the way that local normal direction is computed. Traditionally, the local nor-mal directions are computed using geometric information, such as the average (or weighted) normal of neighboring points or facets surrounding the point to be propagated. In this method, the local nor-mal directions are calculated using equation ~n = ∇φ/|∇φ. φ is the solution of the minimum distance equation, ∇φ · ∇φ = 1, which is a variation of the Eikonal equation. The benefit of calculating normal directions in such a way is that self-intersections are avoided in a natural way. This proposed front propagation method is validated from two aspects: accuracy and efficiency. The proposed front propa-gation technique is successfully applied in the applications of offset surface construction and boundary layer mesh generation. Nomenclature φ The minimum Euclidean distance between any arbitrary point of computational domain to the propagated front ~n Normal vector ∇ First derivative in space Γ The front to be propagated t The sweep counter I.