In this thesis, we consider a projection-based stabilization method for solving buoyancy driven
flows (natural convection problems). The method consists of adding global stabilization for all
scales and then anti-diffusing these effects on the large scales defined by projections into appropriate
function spaces. In this way, stabilization acts only on the small scales. We consider
two different variations of buoyancy driven flows based on the projection-based stabilization.
First, we focus on the steady-state natural convection problem of heat transport through combined
solid and fluid media in a classical enclosure. We present the mathematical analysis of
the projection-based method and prove existence, uniqueness and convergence of the approximate
solutions of the velocity, temperature and pressure. We also present some numerical
tests to support theoretical findings.
Second, we consider a system of combined heat and mass transfer in a porous medium due to
the natural convection. For the semi-discrete problem, a stability analysis of the projectionbased
method and a priori error estimate are given for the Darcy-Brinkman equations in
double-diffusive convection. Then we provide numerical assessments and a comparison with
some benchmark data for the Darcy-Brinkman equations.
In the last part of the thesis, we present a fully discrete scheme with the linear extrapolation
of convecting velocity terms for the Darcy-Brinkman equations.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12613465/index.pdf |
| Date | 01 July 2011 |
| Creators | Cibik, Aytekin Bayram |
| Contributors | Kaya Merdan, Songul |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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