A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers

Fournier, A., Bunge, H.P., Hollerbach, R. and Vilotte, J.P. (2005) A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers. Journal of Computational Physics, 204, pp. 462-489. (doi: 10.1016/j.jcp.204.10.020)

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Abstract

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:UNSPECIFIED
Authors: Fournier, A., Bunge, H.P., Hollerbach, R., and Vilotte, J.P.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
College of Science and Engineering > School of Psychology
Journal Name:Journal of Computational Physics

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