Hybrid meshing using constrained Delaunay triangulation for viscous flow simulations

Abstract

SUMMARYIn this paper, we present a generalized prismatic hybrid meshing method for viscous flow simulations. One major difficulty in implementing a robust prismatic hybrid meshing tool is to handle boundary layer mesh collisions, and normally an extra data structure (e.g. quadtree in two-dimensional and octree in threedimensional) is required. The proposed method overcomes this difficulty via an heuristic approach, and it only relies on constrained delaunay triangulation/tetrahedralization (CDT). No extra data structures are required. Geometrical reasoning is used to approximate the maximum marching distance of each point by walking through the CDT. This is combined with post-processing of marching vectors and distance and prohibition of multilevel differences to form an automatic and robust mechanism to remove boundary layer mesh collisions. Benefiting from the matureness of CDT techniques, the proposed method is robust, efficient and simple to implement. Its capability is demonstrated by generating quality prismatic hybrid meshes for industrial models with complex geometries. The proposed method is believed to be able considerably reduce the effort to implement a robust hybrid prismatic mesh generator for viscous flow simulations.

Hybrid Grid Generation for Viscous Flow Simulations in Complex Geometries

“…Presently, the most prevailing approaches for computing marching directions are those based on the analysis of the manifold of a point [16][17][18][19][20][21]. The manifold of a point here refers to the set of front faces adjacent to the point, and these front faces are thus named manifold faces of that point.…”

“…The solution of that problem could result in the 'best' marching direction at a point by providing an optimal angle property for the next layer of elements that meet at that direction. Nevertheless, it was reported that if the marching direction at each point of a front face was computed in a locally optimal fashion [20,21], it still might not be optimal for the prism carried by the face. Therefore, some kind of global smoothing must be performed after the initial computation of the marching directions.…”

“…It is worth noting that the results of this node classification procedure are very sensitive to the user-specified angle thresholds [20,21]. There also exist some other approaches for computing marching directions.…”

“…Most existing algorithms support increase marching distances slightly at concave corners and vice versa at convex corners in order to smear concave and convex corners and facilitate the marching process. The computation of local curvatures or angle values, based on either the discrete manifold or the original CAD model, is commonly used to determine local marching distances [1,3,21].…”

“…Among those difficulties, those induced by the computations of marching directions and marching distances should be highlighted because both computations determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. A large portion of the efforts involved in the development of a prismatic hybrid mesher were invested in tackling these issues [17][18][19][20][21][22][23].…”