Adaptive multi-patch isogeometric analysis for heat transfer in three-dimensional solid

Abstract

This paper presents an adaptive multi-patch isogeometric framework for modeling heat conduction in isotropic/orthotropic media. The proposed adaptive scheme is a novel combination of local mesh refinement and adaptive time-stepping to improve the calculation efficiency and reduce meshing burden. The local adaptive refinement is driven by a recovery-based error estimator. Truncated hierarchical NURBS (TH-NURBS) are utilized for local adaptive mesh refinement due to their excellent properties, such as linear independence, partition-of-unity, and exact description of complex geometry. Multi-patch technique is applied to model complex structures, with Nitsche’s method as the coupling strategy. The computational accuracy of the proposed model is verified through several 3D numerical examples. The high efficiency of the adaptive scheme is demonstrated by comparing with uniform refinement method and fixed time-stepping method separately.