Compact Spatial Differencing Techniques in Numerical Modeling

Hai-Ru Chang Department of Meteorology, The Pennsylvania State University, University Park, PA 16802

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Hampton N. Shirer Department of Meteorology, The Pennsylvania State University, University Park, PA 16802

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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.

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.

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