Molecular dynamics-based triangulation algorithm of free-form parametric surfaces for computer-aided engineering

Abstract

A new computational approach for automated triangulation of Computer-Aided Design (CAD) surface models, applicable to various CFD (Computational Fluid Dynamics) problems of practical interest is proposed. The complex shaped product configurations are represented by a set of Non-Uniform Rational B-Splines (NURBS) surface patches. The suggested technique is based on the molecular dynamics method. The main idea of the approach is that the mesh nodes are considered as similarly charged interacting particles which move within the region to be meshed under the influence of internal (such as particle–particle interaction forces) and external forces as well as optional additional forces. Moreover, the particles experience a medium resistance due to which the system comes to equilibrium within a relatively short period of time. The proposed 3D surface mesh generation algorithm uses a parametric NURBS representation as initial definition of the domain boundary. This method first distributes the interacting nodes into optimal locations in the parametric domain of the NURBS surface patch using molecular dynamics simulation. Then, the well-shaped triangles can be created after connecting the nodes by Delaunay triangulation. Finally, the mapping from parametric space to 3D physical space is performed. Since the presented interactive algorithm allows to control the distance between a pair of nodes depending on the curvature of the NURBS surface, the method generates high quality triangular mesh. The algorithm enables to produce uniform mesh, as well as anisotropic adaptive mesh with refinement in the large gradient regions. The mesh generation approach has the abilities to preserve the representation accuracy of the input geometry model, create a close relationship between geometry modeling and grid generation process, be automated to a large degree. Some examples are considered in order to illustrate the method’s ability to generate a surface mesh for a complicated CAD model.