A New Fourth-Order Enstrophy and Energy Conserving Scheme
Open Access
- 1 January 1991
- journal article
- Published by American Meteorological Society in Monthly Weather Review
- Vol. 119 (1) , 128-133
- https://doi.org/10.1175/1520-0493(1991)119<0128:anfoea>2.0.co;2
Abstract
A new pseudo-fourth-order finite-difference scheme for the shallow-water and primitive equations is derived. This scheme is a C-grid scheme that conserves energy and conserves enstrophy in the nondivergent limit. The accuracy of the scheme is second order, but in the nondivergent limit it has fourth-order accuracy. In the nondivergent limit, the scheme reduces to Arakawa's fourth-order Jacobian scheme for the vorticity equation for two-dimensional incompressible flow. Model runs with the shallow-water equations are discussed.Keywords
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