A Global Multimoment Constrained Finite-Volume Scheme for Advection Transport on the Hexagonal Geodesic Grid

Abstract

third-order numerical model is developed for global advection transport computation. The multimoment constrained finite-volume scheme has been implemented to the hexagonal geodesic grid for spherical geometry. Two kinds of moments (i.e., point value and volume-integrated average) are used as the constraint conditions to derive the time evolution equations to update the computational variables, which are the values defined at the specified points over each mesh element in the present model. The numerical model has rigorous numerical conservation and third-order accuracy. One of the major merits of the present method is that it does not explicitly involve numerical quadrature, which leads to great convenience in accurately computing curved geometry and source terms. The present paper provides an accurate and practical formulation for advection calculation in the hexagonal-type geodesic grid.