Curvilinear mesh generation using a variational framework. (October 2018) - Turner, Michael; Peiró, Joaquim; Moxey, David
Abstract: We aim to tackle the challenge of generating unstructured high-order meshes of complex three-dimensional bodies, which remains a significant bottleneck in the wider adoption of high-order methods. In particular we show that by adopting a variational approach to the generation process, many of the current popular high-order generation methods can be encompassed under a single unifying framework. This allows us to compare the effectiveness of these methods and to assess the quality of the meshes they produce in a systematic fashion. We present a detailed overview of the theory and formulation of the variational framework, and we highlight how such formulation can be effectively exploited to yield a highly-efficient parallel implementation. The effectiveness of this approach is examined by considering a number of two- and three-dimensional examples, where we show how the proposed approach can be used for both mesh quality optimisation and untangling of invalid high-order meshes. Highlights: We present a method to generate curved meshes using a variational framework. The framework encompasses many existing high-order mesh generation techniques. We outline the mathematical and numerical techniques used in the framework. An efficient parallelisation strategy is presented to increase performance. The framework is applied to a number of two-and three-dimensional examples.