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SUMMARY:Flow-induced Coordinates for Transient Advection-Diffusion Equatio
 ns with Multiple Scales - Konrad Simon (Universität Hamburg)
DTSTART:20170912T143000Z
DTEND:20170912T150000Z
UID:TALK78971@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-author: J&ouml\;rn Behrens		(University of Hamburg\, 
 Germany)        <br></span><br>Simulation over a long time scale in climat
 e sciences as done\, e.g.\, in paleo climate simulations require coarse gr
 ids due to computational constraints. Unresolved scales\, however\, signif
 icantly influence the coarse grid variables. Such processes include (slowl
 y) moving land-sea interfaces or ice shields as well as flow over urbanic 
 areas. Neglecting these scales amounts to unreliable simulation results. S
 tate-of-the-art dynamical cores represent the influence of subscale proces
 ses typically via subscale parametrizations and often employ heuristic cou
 pling of scales. <br><br>Our aim is to improve the mathematical consistenc
 y of the upscaling process that transfers information from the subgrid to 
 the coarse  prognostic scale (and vice-versa). We investigate a new bottom
 -up  techniques for advection dominated problems arising in climate simula
 tions [Lauritzen et al. (2011)]. Our tools are based on ideas for multisca
 le finite element methods for elliptic problems that play a  role in oil r
 eservoir modeling and porous media in general [Efendiev and Hou (2009)\, G
 raham et al. (2012)]. Modifying these ideas is in  necessary in order to a
 ccount for the transient and advection  dominated character which is typic
 al for flows encountered in climate models. <br><span><br>We present a new
  Garlerkin based idea to account for the typical  difficulties in climate 
 simulations. Our modified ideas employ a  change of coordinates based on a
  coarse grid characteristic transform induced by the advection term in ord
 er to account for appropriate subgrid boundary conditions for the multisca
 le basis functions which are essential for such approaches. We present res
 ults from sample runs for a simple advection-diffusion equation with rapid
 ly varying coefficients on several scales.</span>
LOCATION:Seminar Room 1\, Newton Institute
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