Duyff, M. (2006) A numerical bifurcation analysis of flow around a circular cylinder. Master's Thesis / Essay, Mathematics.
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Abstract
Many physical phenomena can be described by partial differential equations (PDEs). Changing the physical parameter in these PDEs will cause changes in the behavior of the system. We are interested in changes of the stability of the state when the physical parameter is varied. (A state is stable if a small perturbation of the state disappears over time.) From these solutions we can make a bifurcation diagram where a characteristic quantity of the state is plotted as function of the physical parameter. There are also ranges of values where the state is not stable. Close to the critical threshold c of the physical parameter where the stability changes, systems become more sensitive, such that small perturbations may trigger some drastic changes in the state. The threshold c is called a bifurcation point. A nice example of a physical system that became unstable is the famous Tacoma Narrows suspension bridge. The bridge collapsed a few months after the opening. The forces of the wind on the bridge led to a transition between purely vertical oscillations and torsional behavior which lead to the collapse of the bridge. To prevent such situations, engineers can perform a bifurcation analysis on such systems. A bifurcation analysis of a system can sometimes be done in a laboratory where a scaled model is build of the system. The physical parameter can be varied and one can see how small changes of the parameters effect the state of the system. This kind of analysis is often very expensive. Nowadays it is also possible to do the bifurcation analysis numerically by simulating a model with the computer. This is much cheaper and it is much easier to change some physical parameters. A numerical bifurcation analysis can be done in two ways: by repeated simulations or by continuation. In the repeated simulation approach, we run the simulation code for different values of and look at the behavior of the system. The second way is to use a continuation technique which will give accurate results on the location of the bifurcation point c.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:28 |
| Last Modified: | 15 Feb 2018 07:28 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/8367 |
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