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Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application in to Atmospheric Simulations

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Authors
Kopera, Michal A.
Giraldo, F.X.
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NUMA2D
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Date of Issue
2013
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Abstract
The resolutions of interests in atmospheric simulations require prohibitively large computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by putting high resolution in crucial areas of the domain. We investigate the performance of a tree-based AMR algorithm for the high order discontinuous Galerkin method on quadrilateral grids with non-conforming elements. We perform a detailed analysis of the cost of AMR by comparing this to uniform reference simulations of two standard atmospheric test cases: density current and rising thermal bubble. The analysis shows up to 15 times speed-up of the AMR simulations with the cost of mesh adaptation below 1% of the total runtime. We pay particular attention to the implicit-explicit (IMEX) time integration methods and show that the ARK2 method is more robust with respect to dynamically adapting meshes than BDF2. Preliminary analysis of preconditioning reveals that it can be an important factor in the AMR overhead. The compiler optimizations provide significant runtime reduction and positively affect the effectiveness of AMR allowing for speed-ups greater than it would follow from the simple performance model.
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Article
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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Applied Mathematics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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