A spectral solenoidal-Galerkin method for rotating thermal convection between rigid plates
type: Item
instance of: scholarly article
title: A spectral solenoidal-Galerkin method for rotating thermal convection between rigid plates
zbMATH Open document ID: 1299.76155
DOI: 10.1155/2013/681246
author: Cihan Yıldırım
author: Durmuş Yarımpabuç
author: Hakan I. Tarman
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 74F10
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 6372922
Wikidata QID: Q59031543
describes a project that uses: Differentiation Matrix Suite
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/681246
OpenAlex ID: W1996648659
cites work: Transition from periodic to chaotic thermal convection
cites work: Q5518219
cites work: Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis
cites work: Cellular convection with finite amplitude in a rotating fluid
cites work: Transition from laminar convection to thermal turbulence in a rotating fluid layer
cites work: Convection in a low Prandtl number fluid layer rotating about a vertical axis
cites work: Hydromagnetic convection in a rotating annulus with an azimuthal magnetic field
cites work: Pattern Formation in the Rotating Cylindrical Annulus with an Azimuthal Magnetic Field at low Prandtl Numbers
cites work: Transition to turbulence in plane Poiseuille and plane Couette flow
cites work: Q3914616
cites work: A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow
cites work: Nonlinear transition in three-dimensional convection
cites work: Different modes of Rayleigh-Bénard instability in two- and three-dimensional rectangular enclosures
cites work: Stability analysis of the flow in a cubical cavity heated from below
cites work: Linearized pipe flow to Reynolds number \(10^7\).
cites work: Chebyshev and Fourier spectral methods.
description: scientific article; zbMATH DE number 6372922