An adaptive discontinuous Galerkin method for modeling cumulus clouds
Giraldo, Francis X.
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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 cloudy and environmental air for the development of a cumulus cloud? A Direct Numerical Simulation of a single cloud is way beyond the capacity of today’s computing power. The use of a Large Eddy Simulation in combination with semi-implicit time-integration and adaptive techniques offers a significant reduction of complexity. So far this work is restricted to dry flow in two-dimensional geometry. The compressible Navier-Stokes equations are discretized using a discontinuous Galerkin method introduced by Giraldo and Warburton in 2008. Time integration is done by a semi-implicit backward difference. For the first time we combine these numerical methods with an h-adaptive grid refinement. This refinement of our triangular grid is implemented with the function library AMATOS and uses a space filling curve approach. Validation through different test cases shows very good agreement between the current results and those from the literature. For comparing different adaptivity setups we developed a new qualitative error measure for the simulation of warm air bubbles. With the help of this criterion we show that the simulation of a rising warm air bubble on a locally refined grid can be more than six times faster than a similar computation on a uniform mesh with the same accuracy.
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