The
choice of the generalized Hamiltonian formulation (the
energy-vorticity theory: EVT) allows us to explore the antisymmetry
of the Poisson and Nambu brackets to obtain consistent spatial
discretisations which allow for
Features of the nonhydrostatic model
The nonhydrostatic atmospheric model is currently under development. Special features intended are:
Model equations arise from energy-vorticity theory (EVT) developed by Peter Névir (FU Berlin).
The prognostic variables will be density ρ, virtual potential temperature density ρθv and the wind vector v whose components are aligned in an Arakawa C/L grid staggering.
The first metric simplification (shallow atmosphere) will be abandoned and the deep atmosphere together with the horizontal Coriolis components will be used. But the spherical shape of the Earth is retained.
The vertical discretisation will make use of a height based terrain-following coordinate system.
The final decision for the temporal discretisation is not yet done: options are fully 3D solver or the HE/VI (horizontally explicit/vertically implicit) approach.
The physical package for the model is intended to take advantage of the large pool of excellent parameterisations available from current models at MPI-M and DWD.
Bracket formulation
The
choice of the generalized Hamiltonian formulation (the
energy-vorticity theory: EVT) allows us to explore the antisymmetry
of the Poisson and Nambu brackets to obtain consistent spatial
discretisations which allow for
consistent energy conversions
conservation of mass, energy and Ertel's potential vorticity
direct control over entropy sources which are all related to dissipation (physical processes) and not to artefacts (aphysical numerical sources and sinks)
Salmon (2005) presented a general approach for retaining the antisymmetic properties of the Nambu brackets in a spatially discretized model. The Arakawa Jacobian is the most known discretisation of this kind.
Our work in recent time (Gassmann and Herzog, 2008) was devoted to the generalized Hamiltonian formulation including turbulence and moisture as well as the specification of the discrete Poisson and Nambu brackets for arbitrary C grids.
Since the use of brackets only gives advise for the spatial discretisation, the time integration scheme could destroy all this nice features. By using the integration by parts rule we found at least for a subproblem a solution. As shown besides, the total domain integrated energy for a vertically traveling sound wave is conserved and conversions between available and kinetic energy are exactly recovered.
For further detailes on this philosphophy for ICON refer to a seminar talk given at NCAR (pdf).
References:
Gassmann, A. and Herzog, H.-J. (2008): Towards a consistent numerical compressible non-hydrostatic model using generalized Hamiltonian tools. Q.J.R.Meterorol.Soc. 134, 1597-1613
Névir, P. (2004): Ertel's vorticity theorems, the particle relabelling symmetry and the energy-vorticity theory for fluid mechanics. Meteorol.Z. 13, 1-14
Névir, P. and Blender, R. (1993): A Nambu representation of incompressible hydrodynamics using helicity and enstrophy. J.Phys. 26A, L1189-L1193
Salmon, R. (2005): A general method for conserving quantities related to potential vorticity in numerical models. Nonlinearity 18, R1-R6
(ags, 27.10.2008)