Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework. (December 2017) - Marco, Onofre; Ródenas, Juan José; Navarro-Jiménez, José Manuel; Tur, Manuel
Highlights: A robust procedure to find intersections between the geometry and the Cartesian mesh. An extended methodology to generate integration subdomains for intersected elements. Exact CAD representation of the boundary considered in the evaluation of integrals. First analysis mesh h -adapted using geometrical data obtained from the intersections. Solution-based h -refinement using an error estimator based on recovery techniques. Abstract: Geometry plays a key role in contact and shape optimization problems in which the accurate representation of the exact geometry and the use of adaptive analysis techniques are crucial to obtaining accurate computationally-efficient Finite Element (FE) simulations. We propose a novel algorithm to generate 3D h -adaptive meshes for an Immersed Boundary Method (IBM) based on Cartesian grids and the so-called NEFEM (NURBS-Enhanced FE Method) integration techniques. To increase the accuracy of the results at the minimum computational cost we seek to keep the efficient Cartesian structure of the mesh during the whole analysis process while considering the exact boundary representation of domains given by NURBS or T-Splines. Within the framework of Cartesian grids, the two significant contributions of this paper are: (a) the methodology used for the mesh-geometry intersection, which represents a considerable challenge due to their independence; and (b) the robust procedure used to generate the integration subdomains that exactly represent the CAD model. The numerical examples given show the proper convergence of the method, its capacity to mesh complex 3D geometries and that Cartesian grid-based IBM can be considered a robust and reliable tool in terms of accuracy and computational cost.