Subdividing triangular and quadrilateral meshes in parallel to approximate curved geometries

A parallel distributed approach to refine a mesh while preserving the curvature of a target geometry is presented. Our approach starts by generating a coarse linear mesh of the computational domain. Second, the former coarse mesh is curved to match the curvature of the target geometry. Then, the curved mesh is partitioned and the subdomain meshes are sent to the slaves. Finally, the curved elements are uniformly subdivided in parallel targeting the geometry approximated by the curved mesh. The result is a distributed finer linear mesh featuring improved geometric accuracy. The key ingredient of our implementation is to approximate the target geometry as a linear mesh equipped with an elemental field corresponding to an element-wise polynomial geometry representation. Thus, the distribution of the curved geometry is equivalent to partitioning the linear mesh and sending the subdomain meshes and the elemental fields to the slaves. The main application of the obtained finer linear mesh is to compute in parallel steady state flow solutions on real topographies. The qualitative results show that for 2D and 3D steady state flow solutions, on real and synthetic topographies, our parallel subdivision approach mitigates the artificial artifacts that might appear with standard straight-sided subdivision methods. We also check the parallel performance of the implementation by performing a weak scalability test in 2D.This work was financially supported by the PRACE project funded in part by the EUs Horizon 2020 research and innovation program (2014-2020) under grant agreement 653838. This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme under grant agreement No 715546. The work of the corresponding author has been partially supported by the Spanish Ministerio de Economía y Competitividad under the personal grant agreement RYC- 2015-01633.Peer Reviewe