Nonlinear Processes in Oceanic and Atmospheric Flows

Presentation

Set Oriented Numerical Methods for the Approximation of Transport Phenomena

Author: Michael Dellnitz, Universitšt Paderborn.

Names and affiliation of other authors:

Oral or poster: Oral presentation

Downloadable talk file:

Set Oriented Numerical Methods for the Approximation

(Cantabria-Dellnitz.ppt, 11549696 bytes)

Abstract:
Over the last years so-called set oriented numerical methods
have been developed in the context of the numerical treatment
of dynamical systems. The basic idea is to cover the objects
of interest -- for instance invariant manifolds or invariant measures-- by outer approximations which are created via adaptive multilevel subdivision techniques. These schemes allow for an extremely memory and time efficient discretisation of the phase space and have the flexibility to be applied to several problem types.

In this talk it will be shown that these numerical techniques can particularly be useful for the approximation of transport phenomena. In this context we will mainly focus on two related applications: first we will analyze the transport of asteroids in the solar system -- this work is mainly motivated by the explanation of the existence of the asteroid belt between Mars and Jupiter. Secondly we will show how to analyze (time dependent) transport phenomena in ocean dynamics. Here we will illustrate the strength of these techniques by a study of transport both in Monterey Bay and in the Antarctic ircumpolar Current.

*Satellite images from NASA and ESA

Nonlinear Processes in Oceanic and Atmospheric Flows. July 2-4, 2008. Castro Urdiales, Cantabria, Spain.