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Discontinuous Galerkin Methods for Adaptive Atmospheric Flow

Friday 24th August 2012 - 11:30 to 12:30
INI Seminar Room 1
In this talk we present higher order discontinuous Galerkin methods for convection dominated problems (using a limiter based stabilization [3]) or diusion dominated problems (see [4]). A comparison of these methods with COSMO, a well established dynamical core for weather forecast, for standard test cases for atmospheric ow [5] is presented. This talk also highlights software techniques as well as recent development of the software package Dune [1] and the discretization module Dune-Fem [2]. In particular we comment on implemented techniques to allows for local grid adaptivity even in parallel environments. In this case dynamic load-balancing is applied to maintain scalability of the simulation code.

References [1] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klofkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A generic grid interface for parallel and adaptive scientic computing. II: Implementation and tests in Dune. Computing, 82(2-3):121{138, 2008.

[2] A. Dedner, R. Klofkorn, M. Nolte, and M. Ohlberger. A Generic Interface for Parallel and Adaptive Scientic Computing: Abstraction Principles and the Dune- Fem Module. Computing, 90(3{4):165{196, 2010.

[3] A. Dedner and R. Klofkorn. A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems. J. Sci. Comput., 47(3):365{388, 2011.

[4] S. Brdar, A. Dedner, and R. Klofkorn. Compact and stable Discontinuous Galerkin methods for convection-diusion problems. Preprint no. 2/2010, Mathematisches Institut, Universitat Freiburg, 2010. accepted for publication in SIAM J. Sci. Comput.

[5] S. Brdar, M. Baldauf, A. Dedner, and R. Klofkorn. Comparison of dynamical cores for NWP models. Theor. Comput. Fluid Dyn., 2012.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons