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Local travelling wave solutions and self-similar solutions for a green roof model

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AlzahraniA_0714_macs.pdf (3.992Mb)
Date
2014-07
Author
Alzahrani, Abdulah
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Abstract
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.
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http://hdl.handle.net/10399/2776
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©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

  • About
  • Copyright
  • Accessibility
  • Policies
  • Privacy & Cookies
  • Feedback
AboutCopyright
AccessibilityPolicies
Privacy & Cookies
Feedback