Monotone advection on the sphere: an Eulerian versus semi-Lagrangian approach

Abstract

The formalism may be used to convert any advection algorithm into the semi-Lagrangian format, and it makes most algorithms sufficient for the integration of flows characterized by large Courant numbers. The formalism is presented in an arbitrary curvilinear system of coordinates. Second, exploiting the generality of the theoretical considerations, the formalism is implemented in solving a practical problem of scalar advection in spherical geometry. The focus is on the alternative of forward-in-time, dissipative finite-difference schemes. This class of schemes offers attractive computational properties in terms of the solutions' accuracy and preservation of a sign or monotonicity. -from Authors