Objectives

Closure models dependent on scale and mathematical model structure

Development of closure models for the effects of unresolved scales which

• are evenly valid for calculations on a grid of variable step width,

• adapt themselves automatically  if the smallest resolved scale begins or stops to mark a certain subprocess in detail,
• in combination with the equations describing the larger scales result in a consistent abstract mathematical model, that owns validity also without relation on a concrete arithmetic grid.

Adaptive numerics of discrete-continuous hybrid models

Development of adaptive numerical methods which consider the structure of the equations of fluid dynamics including closure models.

This includes

• discretization of the equations of fluid dynamics which automatically respect the correct dominant balances in dependence of the resolved length scales and time scales (Hydrostasy, Geostrophy, etc.)
• a mathematically consistent link of the discretization for the numerically resolved scales with the closure models for the unresolved scales,
• generalized convergence concepts and mistake indicators considering model and discretization errors,

• goal-oriented adaptation criteria which allow a control of the adaptation mechanisms in view of the best possible answer of a certain question.

Reference experiments and data basis

Realisation of the reference experiments which fit to the stated application spectrum and permit a successful control for the above mentioned developments. Several theoretical-numerically oriented projects form a group round a limited number of reference experiments. With that is meant beside laboratory also numerical experiments for the purposes of direct numerical simulations.

As far as in the main focus also larger scaled meteorological phenomena are regarded from the theoretical-numerical position, observation dates have to be taken into consideration.
A corresponding cooperation has been already agreed with the Deutscher Wetterdienst (DWD), Potsdam Institute for Climate Impact Research (PIK) and DFG priority programme 1167 ‘Quantitative Precipitation Forecast’.

These research tasks are set in the same manner in a very wide spectrum of uses.
In order to reach a focussing between different single projects in the main task which is necessary for an efficient cooperation, only a limited number of applications relations should be examined in the concrete working programme of the main tasks.