A highly flexible method for constructing the leading and trailing edges of airfoils plays a significant role in the design and optimization of turbomachinery blade profiles. This paper investigates a multi-degree-of-freedom approach for shaping the leading and trailing edges based on the classical NURBS representation framework, incorporating the geometric characteristics of conic sections and circular arcs. The proposed method enables effective control over the leading and trailing edge profiles by flexibly adjusting the slope, taper, and size of the conic section using only a few parameters, while maintaining the aerodynamic chord length of the blade row and ensuring G¹ continuity at the junctions between the fillet curves and the suction/pressure side curves. Control points and weights are computed based on the specified fillet type and central angle to precisely construct conic sections satisfying convex hull requirements. Furthermore, the fillet parameters are linked to the number of blade sections along the spanwise direction, allowing for dynamic variation of the fillet geometry and enabling efficient parametric modeling of complex 3D blade leading and trailing edges. Numerical simulations demonstrate that, compared with the original airfoil, transonic blades incorporating the proposed edge construction method exhibit significantly improved isentropic compression efficiency and a noticeable weakening of shock waves in the leading-edge region.

Tessellation of computer-aided design (CAD) models plays a crucial role in engineering and scientific domains, offering foundational data for model visualization and serving as input for downstream CAD applications, including computer-aided engineering (CAE) and computer-aided manufacturing (CAM). This research presented a rapid tessellation algorithm for CAD models that employs an anisotropic quadtree background grid. The algorithm, constructed from the ground up, guaranteed the output as two-dimensional manifolds. It featureed a size function reliant on curvature and its first derivative to accurately identify geometric featureed within a controllable tolerance during curve discretization. During the adaptive quadtree phase for swift surface tessellation, it minimized mesh elements, ensuring alignment with the original CAD input through a posteriori hybrid multi-order tolerance criteria. Comparative numerical experiments indicate that this algorithm outperforms existing open-source software, such as OCC and Gmsh, and commercial solutions like Ansys, in geometric accuracy, background grid scale, and computational efficiency, highlighting its potential for practical engineering applications.

Delaunay triangulation is a mainly used method for tetrahedral mesh generation, but the initial mesh generated by this method cannot include all boundary constraints, so the boundary recovery is a necessary step for the generation of Delaunay tetrahedral mesh. The difficulty of boundary recovery lies in determining the number and location of auxiliary points (Steiner points) and reducing the negative effects caused by Steiner points. In this study, an improved boundary recovery method for Delaunay tetrahedral mesh generation is proposed, which aims to increase the success rate of constrained recovery and reduce the number of Steiner points added during the boundary recovery. The overall process of this method is composed of a double iteration with two rounds inside, which fully utilizes the advantages of the constrained boundary recovery method and the interior Steiner point insertion method, and reduces the number of broken boundary constraints caused by boundary restoration. This method firstly solves the problem that the recursive shell transformation algorithm tends to fall into the local optimum, by introducing the simulated annealing algorithm, and an improved constrained boundary recovery method is proposed. Then, three key methods, including the AABB tree, the geometrically accurate "line and surface intersection" function, and a hash algorithm for intersection count query, are introduced or proposed to improve the efficiency and robustness of finding the intersection between mesh entities and boundary entities. Finally, for boundaries that cannot be recovered by topological transformation, the interior and boundary Steiner points are inserted. The proposed method is tested on more than 4,000 surface mesh samples of the Thingi10k dataset, which shows that the success rate of constrained boundary recovery is effectively improved, and meanwhile the number of Steiner points introduced by the boundary recovery is generally reduced.

An efficient Advancing Layer Method (ALM) is presented to create semi-structured prisms on viscous walls, in which a procedure that checks possible front intersections is essential to its efficiency. This paper develops various novel schemes to improve the algorithm’s efficiency precisely while not sacrificing its robustness and the resulting mesh quality. First, it employs a set of new techniques, and data structures are developed to improve the efficiency of the front-check procedure. Then, within each octant, a new filter is developed to reduce the intersection computations in the searching process. In addition, data structures are well designed to store the contiguously accessed data in each computing-intensive loop in a contiguous space for a potentially better cache hit ratio. We built a geometry model library formed by examples of industrial complexity to demonstrate the practicability of the algorithm. All the efforts mentioned above enable us to reduce the percentage of computing time taken by intersection check to an acceptable level (approximately 26%), which make it no longer be the most time-consuming part.

Dirty geometry is a geometric model with issues such as normal errors, intersections, slits and overlaps, which are unavoidable for generating meshes directly on the original boundaries. As a result, it is challenging to directly generate topologically compatible surface meshes on dirty geometries, and subsequent numerical analyses can thus be affected. The present study implements a dirty geometry mesh generation algorithm based on tetrahedral meshes, and the core idea of the algorithm is that the surface of an effective tetrahedral mesh must be an effective curved one. Our method performs normal repairment on discrete representations to generate tetrahedral meshes, solves the intersection via cutting tetrahedrons by discrete boundaries, and eliminates slits based on tetrahedron quality optimization. The surface mesh quality is further improved with surface remeshing under the guidance of the geometry size. The view sampling method is used to achieve normal restoration and fulfil the quality requirements in all directions. The multi-level energy thresholds are adopted to improve the efficiency of the tetrahedral optimization. Numerical test results suggest that the present auto-generation algorithm of curved surface meshes on dirty geometries is robust and efficient.