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        Testing refinement criteria in adaptive discontinuous Galerkin simulations of dry atmospheric convection

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        Author
        Muller, Andreas
        Behrens, Jörn
        Giraldo, Francis X.
        Wirth, Volkmar
        Date
        2011
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        Abstract
        A method is introduced which allows one to compare the accuracy between different choices of refinement regions even in a case when the exact solution is not known. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For a rising warm air bubble the average number of elements required for the adaptive simulation is about a factor three times smaller than the number required for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost three times faster than the uniform simulation, and the advantage of adaptive mesh refinement becomes even more pronounced for larger domains. This result suggests that adaptive mesh refinement should have significant potential for future simulations of atmospheric moist convection when the refinement criterion is chosen carefully.
        Description
        Non-hydrostatic Unified Model of the Atmosphere (NUMA)
         
         
        The first NUMA papers appeared in 2008. From 2008 through 2010, all the NUMA papers appearing involved the 2D (x-z slice) Euler equations. All the theory and numerical implementations were first developed in 2D.
         
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        http://hdl.handle.net/10945/38334
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          Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments 

          Muller, Andreas; Behrens, Jorn; Giraldo, Francis X.; Wirth, Volkmar (2012-11-08);
          Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually ...
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          An adaptive discontinuous Galerkin method for modeling cumulus clouds 

          Müller, Andreas; Behrens, Jörn; Giraldo, Francis X.; Wirth, Volkmar (2010-06);
          Theoretical understanding and numerical modeling of atmospheric moist convection still pose great challenges to meteorological research. The present work addresses the following question: How important is mixing between ...
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          Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods 

          Kozdon, J.E.; Wilcox, L. (2013);
          Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel ...
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