Jörn Behrens

Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves

We will present both underlying ideas and concepts, and first results and experiencesgained within an ongoing project to implement a highly memory efficient version of thegrid generator amatos [BRH+05]. Our focus will be on algorithmic and implemen-tational approaches to realize multigrid algorithms on recursively structured adaptivetriangular grids. The key concept is to use a cell-oriented processing of the grids andspace-filling-curve techniques to get rid of the need to store neighbourship relations onadaptive grids.

A parallel adaptive barotropic model of the atmosphere

The parallel adaptive model PLASMA has been developed for modeling a barotropic atmosphere. This model adapts the computational grid at every time step according to a physical error indicator. Thus, compared to uniform grid experiments the number of grid points is reduced significantly. At the same time, the error increases only slightly, when comparing with uniform grid solutions. For the discretization of the underlying spherical shallow water equations a Lagrange-Galerkin method is used. The unstructured triangular grid is maintained by the grid generator amatos and the large linear systems are solved by the parallel solver interface FoSSI. Experimental convergence is shown by means of steady-state and unsteady analytical solutions. PLASMA yields satisfactory results for quasi standard experiments, that is the Rossby-Haurwitz wave and zonal flows over an isolated mountain.

Parallelisierung von Mehrgitteralgorithmen auf der Alliant FX/80

Ein wesentliches Ziel der numerischen Modellierung im Rahmen der Klima-forschung am AWI ist die Beschreibung der Funktion der polaren Ozeane im Gesamtklimasystem. Eine der Standard-Approximationen in numerischen Modellen der ozeanischen Zirkulation ist die „rigid-lid“ Approximation, welche die schnellen Oberflachenwellen des physikalischen Systems aus den Modellen eliminiert Dies ermoglicht einerseits langere Zeitschritte, wie sie fur klimarelevante Probleme unterlaslich sind, andererseits ergibt sich daraus eine zu jedem Zeitschritt der Integration zu losende elliptische Gleichung. Wahrend die ubrigen parabolisch-hyperbolischen Gleichungen relativ einfach zu vektori-sieren und zu parallelisieren sind, erfordert die effiziente Losung des elliptischen Problems eine im Hinblick auf den zur Verfugung stehenden Rechner sehr genaue Auswahl des Losungsverfahrens sowie dessen spezifischer Implementierung. Darin liegt auch der Schwerpunkt dieser Arbeit.

An Adaptive Semi-Lagrangian Advection Model for Transport of Volcanic Emissions in the Atmosphere

The dispersion of volcanic emissions in the Earth atmosphere is of interest for climate research, air traffic control and human wellbeing. Current volcanic emission dispersion models rely on fixed-grid structures that often are not able to resolve the fine filamented structure of volcanic emissions being transported in the atmosphere. Here we extend an existing adaptive semi-Lagrangian advection model for volcanic emissions including the sedimentation of volcanic ash. The advection of volcanic emissions is driven by a precalculated wind field. For evaluation of the model, the explosive eruption of Mount Pinatubo in June 1991 is chosen, which was one of the largest eruptions in the 20th century. We compare our simulations of the climactic eruption on 15 June 1991 to satellite data of the Pinatubo ash cloud and evaluate different sets of input parameters. We could reproduce the general advection of the Pinatubo ash cloud and, owing to the adaptive mesh, simulations could be performed at a high local resolution while minimizing computational cost. Differences to the observed ash cloud are attributed to uncertainties in the input parameters and the course of Typhoon Yunya, which is probably not completely resolved in the wind data used to drive the model. The best results were achieved for simulations with multiple ash particle sizes.