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UID:8433@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140318T110000
DTEND;TZID=Europe/Paris:20140318T120000
DTSTAMP:20241120T210412Z
URL:https://www.i2m.univ-amu.fr/evenements/generalisation-de-la-geometrie-
 magnetique-dans-gysela-developpement-d-un-solver-de-vlasov-poisson-en-4d-p
 our-une-grille-curviligne-arbitraire/
SUMMARY: (...): Généralisation de la géométrie magnétique dans Gysela:
  développement d'un solver de Vlasov-Poisson en 4D pour une grille curvil
 igne arbitraire.
DESCRIPTION:: The large magnetic field in a Tokamak generates a huge anisot
 ropy in the physics along and across magnetic field lines. For this reason
  aligning the grid on the magnetic surfaces and possibly on the magnetic f
 ield lines can considerably increase the accuracy for a given resolution. 
 For Tokamaks with a circular poloidal cross section\, magnetic surfaces ar
 e circular and thus standard toroidal coordinates are naturally aligned on
  magnetic surfaces. This is not the case for more general equilibria with 
 an X-point\, where a numerical definition of the mesh is required. For thi
 s reason\, we need a Vlasov solver that can handle such a mesh.\n\nThe met
 hod of CAO-DAO can help us describe the geometry of magnetic surfaces incl
 uding the X-point.\nIt will give us a mesh of the poloidal plane as a spli
 ne surface. This is defined as a small collection of patches where a logic
 al grid is defined and mapped to the actual computational domain. Each pat
 ch defines a curvilinear grid. We solve all equations in the patch using t
 he coordinate transformation defined by the mapping. So we must develop a 
 numerical method for the Vlasov equation in four dimensional phase-space t
 hat can handle this change of coordinates. Note that the velocity grid rem
 ains cartesian.\n\nThe semi-Lagrangian method consists in two steps: 1) Fo
 llowing the characteristics\, which are particle trajectories\, originatin
 g from grid points\, 2) Interpolating back on the grid. The second step ne
 eds to be performed on the patch. For the first part\, we have three optio
 ns. The first is to move the particles in the physical domain. Then we nee
 d to know the inverse of the change of coordinates in order to transform b
 ack on the patch for interpolation. That could become complicated and cost
 ly because we don't know in general an analytical form for the inverse of 
 the change of coordinates. The second is to move directly all the particle
 s in the patch.\nIn this case\, we need to solve the equations of motion i
 n the patch coordinates\, where they become very involved and more costly 
 to solve. The third option proposed\, and that we have chosen\, is to move
  the positions of the particles in the patch and the velocities of the par
 ticles in the physical domain. With this strategy\, we do not need to know
  the inverse of the change of coordinates and the equations of motion are 
 simpler.\n\nhttps://sites.google.com/site/siteauroreback/\n\nAurore Back\n
 \n
CATEGORIES:Séminaire,Analyse Appliquée
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