Compact Spatial Differencing Techniques in Numerical Modeling

Abstract

The accuracies of the usual centered differencing, compact differencing and finite element methods are compared linearly with a geostrophic adjustment problem and nonlinearly with a vorticity advection problem. The finite element method provides the best approximation in the geostrophic adjustment problem on either a staggered or an unstaggered grid. The compact scheme provides the most accurate representation of the wavenumber distribution for the vorticity advection when the Arakawa Jacobian J7 is used.