Strukturerhaltende Numerik für die Atmosphärendynamik: Ein Zugang im physikalischen Kontext
Main goal of the project ``Structure preserving numerics'' is an improvement of the numerical integration schemes for atmospheric dynamics founded on a physically motivated representation of the equations of motion. Concepts from Analytical Mechanics shall hence be applied to work out Numerical Methods for Meteorological Systems.
An important role play here conservation properties and symmetry principles. The Lagrange-Hamilton representation of atmospheric dynamics contain explicitely energy conservation. A new generalization, Energy-Vorticity-Theorey in Euler-Nambu representation include furthermore vorticity conservation properties. Based on these two representations, numerical methods shall be elaborated in the proposed project, first for multi-layer shallow water models and later on for more sophisticated models too. The subsequent evaluation will show, whether this meets better the conservation aspects.
On the long term perspecitve, this project shall create the base for a physically consistent inclusion also of nonconservative model aspects (e.~g. dissipation, parametrizations). It will be carried out in interdisciplinary cooperation by the work groups for Theoretical Meteorology and Numerical Mathematics.