Conservative shape-preserving two-dimensional transport on a spherical reduced grid

Abstract

A new discretization of the transport equation for two-dimensional transport is introduced. The scheme is two time level, shape preserving, and solves the transport equation in flux form. It uses an upwind-biased stencil of points. To ameliorate the very restrictive constraint on the length of the time step appearing with a regular (equiangular) grid near the pole (generated by the Courant-Friedrichs-Lewy restriction), the scheme is generalized to work on a reduced grid. The method is applied to the test of advection of a coherent structure by solid body rotation on the sphere over the poles. The scheme is shown to be as accurate as current semi-Lagrangian algorithms and is inherently conservative. -Author