Extension of a conservative cascade scheme on the sphere to large courant numbers

The conservative cascade scheme (CCS) combines a one-dimensional mass-conserving finite-volume method with an efficient semi-Lagrangian scheme over the sphere. Major limitations of this scheme are a breakdown in the polar region due to the coordinate singularity and a restriction to polar meridional Courant number C_θ ≤ 1. The proposed scheme is an extension of the CCS over the sphere for C_θ > 1. This is achieved by isolating a region near the pole where the CCS fails and applying a two-dimensional remapping based on the cell-integrated semi-Lagrangian (CISL) scheme. The interface between these two schemes is the singular polar region where the total mass is computed and redistributed in a conservative manner. The resulting scheme is applicable to large polar Courant number and is tested using solid-body rotation and a deformational flow.