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Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado,
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Abstract

The finite-difference scheme for the Laplace and flux-divergence operators described in the companion paper (Part I) is consistent when applied on a grid consisting of perfect hexagons. The authors describe a necessary and sufficient condition for this finite-difference scheme to be consistent when applied on a grid consisting of imperfect hexagons and pentagons, and present an algorithm for generating a spherical geodesic grid on a sphere that guarantees that this condition is satisfied. Also, the authors qualitatively describe the error associated with the operators and estimate their order of accuracy when applied on the new grid.

Abstract

The finite-difference scheme for the Laplace and flux-divergence operators described in the companion paper (Part I) is consistent when applied on a grid consisting of perfect hexagons. The authors describe a necessary and sufficient condition for this finite-difference scheme to be consistent when applied on a grid consisting of imperfect hexagons and pentagons, and present an algorithm for generating a spherical geodesic grid on a sphere that guarantees that this condition is satisfied. Also, the authors qualitatively describe the error associated with the operators and estimate their order of accuracy when applied on the new grid.

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