A fast algorithm for the evaluation of Legendre expansions
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific Computing
A spectral element basin model for the shallow water equations
Journal of Computational Physics
An analysis of the fractional step method
Journal of Computational Physics
A pseudospectral approach for polar and spherical geometries
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
A fast spherical filter with uniform resolution
Journal of Computational Physics
Fast Shallow-Water equation solvers in latitude-longitude coordinates
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
Computational harmonic analysis for tensor fields on the two-sphere
Journal of Computational Physics
A performance comparison of associated Legendre projections
Journal of Computational Physics
An efficient spectral-projection method for the Navier--Stokes equations in cylindrical geometries
Journal of Computational Physics
A three-dimensional spectral element model for the solution of the hydrostatic primitive equations
Journal of Computational Physics
Journal of Computational Physics
The Fastest Fourier Transform in the West
The Fastest Fourier Transform in the West
The choice of spectral element basis functions in domains with an axis of symmetry
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Hi-index | 31.45 |
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.