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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 681246, 8 pages
Research Article

A Spectral Solenoidal-Galerkin Method for Rotating Thermal Convection between Rigid Plates

1Mechanical Engineering Department, Akdeniz University, Antalya 07058, Turkey
2Mathematics Department, Osmaniye Korkut Ata University, Osmaniye 80000, Turkey
3Engineering Sciences Department, Middle East Technical University, Ankara 06531, Turkey

Received 18 January 2013; Accepted 21 February 2013

Academic Editor: Safa Bozkurt Coskun

Copyright © 2013 Cihan Yıldırım et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of thermal convection between rotating rigid plates under the influence of gravity is treated numerically. The approach uses solenoidal basis functions and their duals which are divergence free. The representation in terms of the solenoidal bases provides ease in the implementation by a reduction in the number of dependent variables and equations. A Galerkin procedure onto the dual solenoidal bases is utilized in order to reduce the governing system of partial differential equations to a system of ordinary differential equations for subsequent parametric study. The Galerkin procedure results in the elimination of the pressure and is facilitated by the use of Fourier-Legendre spectral representation. Numerical experiments on the linear stability of rotating thermal convection and nonlinear simulations are performed and satisfactorily compared with the literature.