期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 204, 期 2, 页码 462-489出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2004.10.020
关键词
rotating fluids; Boussinesq equations; Fourier-spectral element method; cylindrical coordinates; pole conditions
We present a Fourier-spectral element approach for modeling thermal convection in a rotating axisymmetric container. Following the theory detailed in Bernardi et al. [C. Bernardi, M. Dauge, Y. Maday, Spectral Methods for Axisymmetric Domains, Gauthier-Villars, Paris, 1999], a Fourier expansion of the field variables is performed in the periodic direction, and the resulting collection of meridional problems is discretized by means of a parallel spectral element method. A Gauss-Lobatto-Jacobi (0,1) quadrature, which incorporates the cylindrical radius in its weight, is introduced to avoid a potential degeneracy of the discrete set of equations, due to those nodes located on the axis of symmetry. A second-order timestepping scheme is presented, which treats the Coriolis and viscous forces implicitly. Numerical comparisons with analytical and published numerical solutions in spherical and cylindrical geometries are presented which highlight the accuracy of the model and demonstrate its spectral convergence properties. (c) 2004 Elsevier Inc. All rights reserved.
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