Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part I

Abstract

he design of accurate, conservative, consistent, and monotone operators for remapping scalar fields between computational grids on the sphere has been a persistent issue for global modeling groups. This problem is especially pronounced when mapping between distinct discretizations (such as finite volumes or finite elements). To this end, this paper provides a novel unified mathematical framework for the development of linear remapping operators. This framework is then applied in the development of high-order conservative, consistent, and monotone linear remapping operators from a finite-element discretization to a finite-volume discretization. The resulting scheme is evaluated in the context of both idealized and operational simulations and shown to perform well for a variety of problems.