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Adaptive mesh refinement for a 2D unified continuous/discontinuous Galerkin Non-hydrostatic Atmospheric Model

Presented by: 
Michal A. Kopera & Frank X. Giraldo Naval Postgraduate School
Date: 
Thursday 25th October 2012 - 10:30 to 10:55
Abstract: 
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 [1], [2], [3] 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 [4] have been specifically designed to handle the IMEX methods with AMR.

[1] A. Muller, J. Behrens, F.X. Giraldo, V. Wirth (2011). An Adaptive Discontinuous Galerkin Method for Modelling Atmospheric Convection. Defense Technical Information Center Report, http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA546279

[2] S. Blaise, and A. St-Cyr (2011). A Dynamic hp-Adaptive Discontinuous Galerkin Method for Shallow-Water Flows on the Sphere with Application to a Global Tsunami Simulation, Monthly

[3] M. A. Kopera and F.X. Giraldo (2012). AMR for a 2d DG Nonhydrostatic atmospheric model, in preparation.

[4] L.E. Carr, C.F. Borges, and F.X. Giraldo (2012). An element-based spectrally-optimized approximate inverse preconditioner for the Euler equations, SIAM J. Sci. Comp. (in press).
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons