Towards adaptive mesh refinement for the spectral element solver Nek5000

When performing computational fluid dynamics (CFD) simulations of complex flows, the a priori knowledge of the flow physics and the location of the dominant flow features are usually unknown. For this reason, the development of adaptive remeshing techniques is crucial for large-scale computational problems. Some work has been made recently to provide Nek5000 with adaptive mesh refinement (AMR) capabilities in order to facilitate the generation of the grid and push forward the limit in terms of problem size and complexity. Nek5000 is an open-source, highly scalable and portable code based on the spectral element method (SEM), which offers minimal dissipation and dispersion, high accuracy and nearly exponential convergence. It is aimed at solving direct numerical simulations of turbulent incompressible or low Mach-number flows with heat transfer and species transport. The approach chosen for adapting the mesh is the h-refinement method, where elements are split locally, which requires the relaxation of the conforming grid constraint currently imposed by Nek5000. Other challenges include the implementation of an efficient management of the grid as refinement is applied, the development of tools to localize the critical flow regions via error estimators and the extension of the current preconditioning strategy to non-conforming grids. In this paper, we present a new procedure to setup an algebraic multigrid solver used as part of the preconditioner for the pressure equation.