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SUMMARY:Accuracy of adaptive discontinuous Galerkin simulations - Andreas 
 Mller\,   (Naval Postgraduate School)
DTSTART:20120925T132500Z
DTEND:20120925T135000Z
UID:TALK40089@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Adaptive mesh refinement generally serves to increase computat
 ional efficiency without compromising the accuracy of the numerical soluti
 on significantly. However it is an open question in which regions the spat
 ial resolution can actually be coarsened without affecting the accuracy of
  the result significantly. This question is investigated for a specific ex
 ample of dry atmospheric convection\, namely the simulation of warm air bu
 bbles. For this purpose a novel numerical model is developed that is tailo
 red towards this specific meteorological problem. The compressible Euler e
 quations are solved with a Discontinuous Galerkin method. Time integration
  is done with a semi-implicit approach and the dynamic grid adaptivity use
 s space filling curves via the AMATOS function library. The numerical mode
 l is validated with a convergence study and five standard test cases. \n\n
 A method is introduced which allows one to compare the accuracy between di
 fferent choices of refinement regions even in a case when the exact soluti
 on is not known. Essentially this is done by comparing features of the sol
 ution that are strongly sensitive to spatial resolution. For a 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 50% smaller than the number used for the simu
 lation with the uniform fine-resolution grid. Correspondingly the adaptive
  simulation is almost two times faster than the uniform simulation.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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