Structure preserving numerics for atmospheric dynamics: A physics based approach

• Applicants: Privatdozent Dr. Peter Névir; Professor Dr.-Ing. Sebastian Reich
• Subject Area: Atmospheric Science
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 32520616

Principal goal of the project ¿Structure Preserving Numerics¿ is the development of improved numerical integration schemes for atmospheric dynamics based on physically motivated representations and approximations to the governing equations of motion. Concepts from Analytical Mechanics are to be applied to derive novel numerical methods. It is well understood that conservation properties play an important role in atmospheric dynamics. The Lagrange-Hamilton representation of atmospheric dynamics contains energy conservation explicitly and conservation of vorticity implicitly via symmetry arguments. A new generalization, the Energy-Vorticity-Theory in Euler-Nambu representation, includes both vorticity and energy conservation properties in an explicit manner. Based on these two representations, numerical methods will be developed; first for multi-layer shallow water models and, at a later stage, for more complex model systems. Extensive testing will demonstrate to what extent better numerical conservation properties lead to improved model dynamics. On a long term perspective, the project will also create the foundation for a physically consistent inclusion of nonconservative model aspects (e.g. dissipation, parametrizations). It will be carried out in interdisciplinary collaboration between Theoretical Meteorology and Numerical Mathematics.

• DFG Programme: Research Grants