Conservative Leap-Frog + Asselin filter

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Object:

Introduce in the trunk the modified Leap-Frog + Robert-Asselin filter time stepping scheme (thereafter LF-RA) described in (Leclair and Madec Ocean Modelling 2009, in press). The scheme allows a exact conservation of the heat and salt contents when using variable volume thickness (key_vvl). The non-conservation of the standard LF-RA due to the time diffusion of the forcing through the filter. In the modified scheme the exact conservation is achieved by removing the forcing from the filter. This requires 3 modifications, on the forcing evaluation, on its time discretisation, and on the filter, resp. :

• Forcing evaluation : the momentum and tracers forcing are evaluated at kt+1/2, no-more at kt.
  
• Forcing time discretisation : 0.5 * ( Q(k+1/2) + Q(kt-1/2) ), instead of simply Q(kt).
  
• Filter : the RA filter no-more act on the forcing, i.e. -afp * rdt * ( Q(kt+1/2) - Q(kt-1/2) ) is removed from the filter
  

Status:

ongoing work (NEMO-Paris).

Module involved:

fldread.F90 sbcmod.F90 ; trasbc.F90 , traqsr.F90 , dynzdf_exp.F90 , dynzdf_imp.F90 sshnxt.F90 , tranxt.F90 , dynnxt.F90

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1. Forcing evaluation

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2. Forcing time discretisation

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3. Modified filter

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