Stability Conditions for an Alternated Grid in Space and Time

The stability conditions of a staggered lattice in space and time are derived. The grid used is known as the Eliassen grid (Eliassen 1956). It is shown that the stability conditions of the shallow water wave equations, for this type of lattice, have essentially the same stability condition as the unstaggered grid and Arakawa's B and C lattice. Upon implementation of a leapfrog scheme in a staggered grid in space and time, there will be no computational modes. No smoothing is needed to compute the Coriolis (gravity wave) terms as required in Arakawa's C (B) grid. Furthermore, the usage of an Eliassen grid halves the computation time required in Arawaka's B or C grid (Mesinger and Arakawa 1976). Therefore, there are fundamental advantages for the usage of an alternated grid in space and time.

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