Adaptive mesh refinement for a 2D unified continuous/discontinuous Galerkin Non-hydrostatic Atmospheric Model
The adaptive mesh refinement techniques for element-based Galerkin methods are becoming a strong candidate for future numerical weather prediction models. Particular attention has been paid to the discontinuous Galerkin method , ,  as it avoids global assembly of data and makes the implementation of the algorithm easier. In this presentation we will focus on the extension of the 2D discontinuous Galerkin, quad-based non-conforming adaptive mesh refinement algorithm to a continuous Galerkin formulation. The novelty of this approach is that we propose to do this within a unified CG/DG nonhydrostatic atmospheric model that we call NUMA (Nonhydrostatic Unified Model of the Atmosphere). NUMA is equipped to handle AMR at various levels: IMEX time-integrators are used to be able to use large time-steps and a new class of preconditioners  have been specifically designed to handle the IMEX methods with AMR.
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