<p>We are interested in backward-in-time solution techniques for evolutionary PDE problems
arising in fluid mechanics. In addition to their intrinsic interest, such techniques have
applications in recently proposed retrograde data assimilation. As our model system we
consider the terminal value problem for the Kuramoto-Sivashinsky equation in a l D periodic
domain. The Kuramoto-Sivashinsky equation, proposed as a model for interfacial
and combustion phenomena, is often also adopted as a toy model for hydrodynamic turbulence
because of its multiscale and chaotic dynamics. Such backward problems are typical
examples of ill-posed problems, where any disturbances are amplified exponentially during
the backward march. Hence, regularization is required to solve such problems efficiently in
practice. We consider regularization approaches in which the original ill-posed problem is
approximated with a less ill-posed problem, which is achieved by adding a regularization
term to the original equation. While such techniques are relatively well-understood for
linear problems, it is still unclear what effect these techniques may have in the nonlinear
setting. In addition to considering regularization terms with fixed magnitudes, we also
explore a novel approach in which these magnitudes are adapted dynamically using simple
concepts from the Control Theory.</p> / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21765 |
| Date | January 2007 |
| Creators | Gustafsson, Jonathan |
| Contributors | Protas, Bartosz, Computational Engineering and Science |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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