Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves.
The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/335798 |
| Date | 09 November 2014 |
| Creators | Faria, Luiz |
| Contributors | Kasimov, Aslan R., Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Samtaney, Ravi, Ketcheson, David I., Keyes, David E. |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Rights | 2015-11-09, At the time of archiving, the student author of this dissertation opted to temporarily restrict access to it. The full text of this dissertation became available to the public after the expiration of the embargo on 2015-11-09. |
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