Towards a Volume Mesh Generator Tailored for NEFEM

The conversion of digital models from computer-aided design (CAD) to meshes for computer-aided engineering (CAE) is a well-known bottleneck, because of the amount of human intervention required in the cumbersome de-featuring process. This paper introduces the strategy to address this issue by generating the geometric-persistent volume mesh tailored for the NURBS-enhanced finite element method (NEFEM). The NEFEM has been developed to decouple the geometry representation and the numerical approximation to address this issue. NEFEM uses CAD data, the non-uniform rational B-spline (NURBS) that describe the boundary representation (B-rep), to describe the geometry of the computational domain, and it adopts polynomial shape functions for the numerical approximation of the unknown solution. The need for de-featuring is avoided by NEFEM, and the geometric error is completely removed. As a dedicated NEFEM mesh generator is crucial for problems involving complex geometries, this paper introduces the strategy devised to generate volume meshes tailored for NEFEM solvers. The proposed approach is based on previously developed NEFEM surface mesh generation method, and new requirements for validity checks are imposed for the volume mesh generation. A layer of NEFEM volume elements is firstly created, followed by the interior volume mesh which can be obtained from a standard mesh generator. The resulting mesh maintains the exact geometric B-rep, and the element sizes are fully dominated by the user-defined spacing and not by the presence of small geometric features. Examples are presented for an illustrative demonstration of the proposed technique.