The advancement of knowledge in geosciences heavily depends on modeling and computer simulation. A key to our future projections on climate change, risk analysis in natural hazards, and even process description of basic natural phenomena like cloud formation is the mathematical description of the underlying physical, chemical, and biological processes. Subsequently, the corresponding equations need to be solved by numerical methods suited for implementation on high-performance computers.
An unsolved question in these simulations is the correct description and numerical representation of multi-scale processes. These are for example, the influence of small-scale mixing and entrainment processes of moist air at cloud boundaries on the development of the entire cloud cluster, the interaction of long tsunami waves with highly complex topography, or the trigger of large-scale wave phenomena from small-scale perturbations (the butterfly effect). One of our key objectives is therefore the development of Adaptive Multi-Scale Methods.
In order to capture these effects, adaptive numerical methods are developed, which are capable of detecting areas needing high resolution on the fly, and adapting to these dynamical processes automatically. This automatic adaptation demands for highly accurate and robust numerical methods, which - applied to geophysical fluid dynamics problems - form the Numerical Methods for Geophysical Fluid Dynamics focus of the group’s work. Furthermore, efficient implementation of these demanding methods on high-performance computers including large numbers of processors is a must and new techniques for achieving scalability and efficiency are being developed and are the objective of Efficient Algorithms for High Performance Computing developments.
The CliSAP research group (CRG) 'Numerical Methods in Geosciences' develops new methods to improve the accuracy and reliability of simulations in oceanography, meteorology, and glaciology in an intelligent way.
- Beckers, S., Behrens, J., & Wollner, W. (2019). Duality based error estimation in the presence of discontinuities. Applied Numerical Mathematics, 144, 83-99. doi:10.1016/j.apnum.2019.05.016.
- Behrens, J. (2016). Numerical methods and scientific computing for climate and geosciences. In W. König (
Ed.), Mathematics and Society (pp. 281-293). Zürich: European Mathematical Society Publ. House. doi:10.4171/164-1/15.
- Beisiegel, N., & Behrens, J. (2015). Quasi-nodal third-order Bernstein polynomials in a discontinuous Galerkin model for flooding and drying. Environmental Earth Sciences, 74(11), 7275-7284. doi:10.1007/s12665-015-4745-4.