Zhoufang Xiao

Tetrahedral mesh improvement by shell transformation

Existing flips for tetrahedral meshes simply make a selection from a few possible configurations within a single shell (i.e., a polyhedron that can be filled up with a mesh composed of a set of elements that meet each other at one edge), and their effectiveness is usually confined. A new topological operation for tetrahedral meshes named shell transformation is proposed. Its recursive callings execute a sequence of shell transformations on neighboring shells, acting like composite edge removal transformations. Such topological transformations are able to perform on a much larger element set than that of a single flip, thereby leading the way towards a better local optimum solution. Hence, a new mesh improvement algorithm is developed by combining this recursive scheme with other schemes, including smoothing, point insertion, and point suppression. Numerical experiments reveal that the proposed algorithm can well balance some stringent and yet sometimes even conflict requirements of mesh improvement, i.e., resulting in high-quality meshes and reducing computing time at the same time. Therefore, it can be used for mesh quality improvement tasks involving millions of elements, in which it is essential not only to generate high-quality meshes, but also to reduce total computational time for mesh improvement.

An improved local remeshing algorithm for moving boundary problems

ABSTRACT Three issues are tackled in this study to improve the robustness of local remeshing techniques. Firstly, the local remeshing region (hereafter referred to as ‘hole’) is initialized by removing low-quality elements and then continuously expanded until a certain element quality is reached after remeshing. The effect of the number of the expansion cycle on the hole size and element quality after remeshing is experimentally analyzed. Secondly, the grid sources for element size control are attached to moving bodies and will move along with their host bodies to ensure reasonable grid resolution inside the hole. Thirdly, the boundary recovery procedure of a Delaunay grid generation approach is enhanced by a new grid topology transformation technique (namely shell transformation) so that the new grid created inside the hole is therefore free of elements of extremely deformed/skewed shape, whilst also respecting the hole boundary. The proposed local remeshing algorithm has been integrated with an in-house unstructured grid-based simulation system for solving moving boundary problems. The robustness and accuracy of the developed local remeshing technique are successfully demonstrated via industry-scale applications for complex flow simulations.

Booleans of triangulated solids by a boundary conforming tetrahedral mesh generation approach

A new algorithm is proposed to recast Boolean operations of triangulated solids as a boundary conforming tetrahedral meshing problem. Different from those existing algorithms that merely maintain a conforming surface mesh, the new algorithm maintains a boundary conforming volume mesh at the same time of computing surface intersections. This volume mesh not only provides a background structure in helping the improvement of the efficiency of intersection computations, but also enables the development of a set of efficient and reliable flood-filling type procedures to extract the Boolean outputs. The efficiency and robustness of the proposed algorithm are investigated in further details, and various techniques are suggested to tackle these two issues accordingly. Finally, the performance of the proposed algorithm has been evaluated by performing suitable test cases and the results are compared well with those data obtained by other state-of-the-art codes. Graphical abstractDisplay Omitted HighlightsBoolean operations are recast as a boundary conforming tetrahedral meshing problem.A volume mesh is maintained at the same time of surface repairing.The volume mesh could help reduce time costs of searching intersecting entities.Efficient flood-filling procedures are adopted to extract Boolean outputs.

Automatic surface repairing, defeaturing and meshing algorithms based on an extended B-rep

A new data structure that combines the continuous and discrete surface representations is proposed.A sequence of repairing, defeaturing and meshing algorithms that can exploit the strengths of both representations is developed.The repairing algorithm is defined on the discrete model but can output a correct B-rep.The output mesh is loyal to the input continuous model and therefore more geometrically accurate. This paper presents an extended surface boundary representation (B-rep), where each topology entity can have dual geometric representations to accommodate various defects (e.g., gaps and overlaps) commonly present in CAD models. Keeping a uniform B-rep and the unsuppressed geometry data enables the use of various existing repairing, defeaturing and meshing algorithms to process CAD models with small gaps and overlaps on surface boundaries. The continuous geometry of the input model remains untouched in the repairing, defeaturing and meshing process, and the output mesh is loyal to this geometry. Such feature is often desirable in numerical simulations that require meshes with high geometry fidelity.