Applied Mathematics and Computational Physics

Group leader: Peter Korn

 

The Applied Mathematics and Computational Physics group (AMCP) is devoted to the study of Numerical Geophysical Fluid Dynamics and performs research on the fluid dynamical kernel of atmosphere and ocean models. AMCP is located at the interface between Applied Mathematics, Atmosphere/Ocean science and scientific computing. While rooted in Applied Mathematics the group reaches out to Atmosphere/Ocean science as well as computational science. We explore methods from Mathematical Fluid Dynamics, Numerical Analysis and from Computational Fluid Dynamics and try to gain insight from numerical experiments, theoretical considerations and the interplay between both.


The current scientific focus of the group is centered around a primary and a secondary theme:

Ocean Model Development and Numerical Geophysical Fluid Dynamics
Developing structure preserving discretization methods for the oceanic Primitive Equations: This is performed in the framework of MPI-M's internal project ICON. The architecture of modern supercomputers suggest for performance reasons the use of nearly uniform grids for the tessellation of the Earth. This excludes traditional latitude-longitude grids and leads to so-called unstructured grids, such as the icosahedral grid that we are using in ICON.  An additional design goal is the option to deliberately break the near-uniformity of the grid by local grid refinement in order to obtain an improved solution in a region of interest. These grid requirements pose individually as well as combined fundamental challenges on the discretization of the dynamical core. Our attempt to meet this challenge consists in the development of structure preserving discretizations. This type of (spatial) discretization is also known under the name mimetic or physics compatible discretization. Structure preserving methods aim at embedding a physical concept into a numerical model. They intend to improve the quality of the simulations by formulating discrete equivalents of essential properties of continuum physics.

Find Meaning in Errors
Estimating errors for geophysically relevant diagnostics: Errors are the amount to which an approximation of a physically relevant goal such as energy or transported volume deviates from the true value. We assume here that the approximation does perfectly what it should, that means errors are not mistakes or bugs, and that with error we are referring to a inherent limitation of the approximation. This kind of fundamental limitation may getting smaller by improving the approximation but is never completely vanishing. We have to accept the fact that errors are inevitable, simply because they contain what we do not know. We respond to that fact in two ways, first by looking for meaning and structure in errors and second by quantifying errors via developing methods that allow to calculate errors bars.