Smooth quasi‐homogeneous gridding of the sphere

We describe a variational technique for generating smooth quasi-homogeneous numerical grids covering the sphere. This work extends our earlier studies of non-standard global grids by relaxing the requirement of conformality to admit a greater degree of homogeneity. The motivation for this extension is to increase the minimum grid distance and thus to enable a larger time step to be used within an Eulerian grid-point model. The grids described here are specified by balancing terms in a variational principle that penalizes departures of grid-point density from smoothness and homogeneity. Grids generated by the new procedure are tested in both the cubic and octagonal configurations we have described in our earlier studies. The time-step restriction is successfully alleviated without significant loss of solution accuracy.