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SUMMARY:Multilevel time integrators for large-scale atmospheric flows - Be
 nacchio\, T (Freie Universitt Berlin)
DTSTART:20121004T090000Z
DTEND:20121004T093000Z
UID:TALK40452@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The fluid dynamically most comprehensive mathematical model of
  the atmosphere\, the Euler equations\, admits solutions driven by compres
 sibility\, buoyancy\, and inertia. In the low Mach number case there is a 
 scale separation of the three effects\, and reduced sets of equations have
  been developed from the fully compressible model to describe the differen
 t regimes. In a context of increasing computing resources\, reliable discr
 ete solvers have to be devised\, which can resolve the different scales an
 d conserve of physical quantities as mass and total energy. As for the tim
 e discretization\, one faces the choice between the stability-constrained 
 explicit methods and the unconditionally stable\, but costly and overdispe
 rsive implicit methods. Semi- implicit methods aim at exploiting the advan
 tages of the two approaches as well as reducing their weak points. The goa
 l of the work we present is to obtain a second-order accurate method to re
 produce multiscale features of solutions of the fully compressible equatio
 ns\, filtering unwanted small-scale disturbances but retaining the propert
 ies of significant waves. An anelastic code for small-scale flows discreti
 sed with a projection method is extended with the insertion of an implicit
  pressure term\; as a result\, an additional zero-order term is added to t
 he Poisson equation for the pressure in the correction step. On one hand\,
  the approach is in agreement with a standard discretisation of the wave e
 quation for the pressure\; on the other hand\, the discretisation reduces 
 to the anelastic one for vanishing Mach number. Preliminary runs on advect
 ion test cases confirm the feasibility of the approach\; large-scale tests
  will be performed with the insertion of the Coriolis term and the adoptio
 n of a suitable spherical grid. Then\, a multilevel time discretisation ba
 sed on multigrid techniques will enable to simulate multiscale test cases\
 , thereby paving the way for an accurate and efficient all-speed solver.\n
LOCATION:Seminar Room 1\, Newton Institute
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