Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments

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Author
Muller, Andreas
Behrens, Jorn
Giraldo, Francis X.
Wirth, Volkmar
Date
2012-11-08Metadata
Show full item recordAbstract
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.
Description
Accepted by the Journal of Computational Physics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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