In this thesis we study travelling wave solutions and self-similar solutions for a green roof model and for some simpler models which are derived from that model. We focus on two limiting cases near a dry region and near a saturated region. We start by considering a convection model in the absence of diffusion and sink terms. We show that rarefaction waves and shock solutions exist for several cases. Next, we consider a convection-diffusion model where both the convective and diffusive terms are present and we show that travelling wave solutions and self-similar solutions exist for some cases. Moreover, numerical simulations are used for the travelling wave and self-similar solutions and confirm the analytic predictions. Finally, we consider the green roof model where all terms are present and we show that travelling wave solutions exist, whereas self-similar solutions are not found. We also show the travelling wave solutions exist for the two limiting cases.
Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:650553 |
Date | January 2014 |
Creators | Alzahrani, Abdulah |
Contributors | Lacey, Andrew; Banas, Lubomir |
Publisher | Heriot-Watt University |
Source Sets | Ethos UK |
Detected Language | English |
Type | Electronic Thesis or Dissertation |
Source | http://hdl.handle.net/10399/2776 |
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