1:45 PM - 2:00 PM
[AAS01-01] A nestable, multigrid-friendly grid on a sphere for global spectral models based on Clenshaw-Curtis quadrature
Keywords:Numerical Weather Prediction, global spectral model, multigrid method
The nestable nature of the proposed grid will allow for a straightforward implementation of a pseudo-spectral multigrid method without any complicated off-grid interpolation in solving the non-constant Helmholtz equation that results from semi-implicit time stepping. The proposed grid can be further adapted to take a structured form, such as the icositetraheadral (24-face polyhedral) grid (Figure d), by adjusting the number of longitudinal gridpoints and the longitude of the first gridpoint of each latitude circle. We postulate that employing the pseudo-spectral multigrid method will foster smooth and gradual transition from spectral modelling to grid-based (or grid/spector hybrid) modelling since the grid-space representation of the horizontal derivatives evaluated by the pseudo-spectral method can be readily replaced by local horizontal derivatives evaluated by some grid-based scheme such as finite difference, finite volume, or finite/spectral element method. Given that grid-based elliptic solvers tend to be less efficient at larger scale, a grid/spector hybrid approach, where a grid-based multigrid method with shallow layers is combined with a spectral elliptic solver used only at the coarsest grid with moderate resolution, seems a reasonable strategy that compromises the need to avoid global inter-node communications and to maintain acceptable accuracy and fast convergence rate.