Adaptive Discontinuous Galerkin Method for Modeling Atmospheric Convection (Preprint)

摘要

Theoretical understanding and numerical modeling of atmospheric moist convection still pose great challenges to meteorological research. A Direct Numerical Simulation of a single cumulus cloud is 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. This paper presents a first step towards an efficient simulation of a single cloud. So far this work is restricted to dry flow in two- dimensional geometry without subgrid-scale modeling. The compressible Euler 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 formula. This paper represents the first application of a triangular discontinuous Galerkin method with h-adaptive grid refinement for nonhydrostatic atmospheric flow. This refinement of our triangular grid is implemented with the function library AMATOS and uses an efficient 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 four times faster than a similar computation on a uniform mesh while still producing the same accuracy. Remarkably only 5% of the total CPU time is used for adapting the grid after each time-step.