On staggering techniques and the non-staggered Z-grid scheme

A new staggered-grid momentum-based numerical scheme that is equivalent to the non-staggered Z-grid scheme for linearized shallow water equations is proposed. Utilizing the equivalence between the staggered/non-staggered discrete vorticity-divergence fields and the discrete velocity fields, the equivalent vorticity-divergence formulations of some of the existing staggered-grid schemes, namely the C-grid, D-grid, CD-grid, and co-volume schemes are derived. The strengths and weaknesses of these schemes are discussed from the perspectives of their new formulations.

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