Testing Refinement Criteria in Adaptive Discontinuous Galerkin Simulations of Dry Atmospheric Convection
Abstract
Adaptive mesh refinement generally serves 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 be coarsened without affecting the accuracy of the result. This question is investigated for a specific meteorological problem, namely the simulation of atmospheric convection. For this purpose a novel numerical model is developed that is tailored towards this specific meteorological problem. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with a semiimplicit approach and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. So far the model is able to simulate dry flow in two-dimensional geometry without subgrid-scale modeling. The model is validated with three standard test cases. 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 22, 2011
- Accession Number
- ADA558867
Entities
People
- Andreas Mueller
- Francis Giraldo
- Joern Behrens
- Volkmar Wirth
Organizations
- Naval Postgraduate School