Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments
Giraldo, Francis X.
MetadataShow full item record
Adaptive mesh refinement generally aims 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 example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with an IMEXmethod 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 tested with three standard test cases. An error indicator is introduced for a warm air bubble test case which allows one to compare the accuracy between different choices of refinement regions without knowing the exact solution. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For the rising warm air bubble the additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about a factor of two times smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU-time.
Accepted by the Journal of Computational Physics
Showing items related by title, author, creator and subject.
Testing refinement criteria in adaptive discontinuous Galerkin simulations of dry atmospheric convection Muller, Andreas; Behrens, Jörn; Giraldo, Francis X.; Wirth, Volkmar (2011);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 ...
Evaluation of the utility of static and adaptive mesh refinement for idealized tropical cyclone problems in a spectral element shallow water model Hendricks, Eric A.; Kopera, Michal A.; Giraldo, Francis X.; Peng, Melinda S.; Doyle, James D.; Jiang, Qingfang (2015-04-09);The utility of static and adaptive mesh refinement (SMR and AMR, respectively) are examined for idealized tropical cyclone (TC) simulations in a spectral element f-plane shallow water model. The SMR simulations have varying ...
Müller, Andreas; Behrens, Jörn; Giraldo, Francis X.; Wirth, Volkmar (2010-06);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 ...