Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application to Atmospheric Simulations
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
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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 signi cant runtime reduction and positively a ect the e ectiveness of AMR allowing for speed-ups greater than it would follow from the simple performance model.
- Atmospheric Physics
- Numerical Mathematics