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Stability of a FBTCS scheme applied to the propagation of shallow-water inertia-gravity waves on various space grids
Beckers, J.-M.; Deleersnijder, E. (1993). Stability of a FBTCS scheme applied to the propagation of shallow-water inertia-gravity waves on various space grids. J. Comput. Physics 108(1): 95-103
In: Journal of Computational Physics. Academic Press: Amsterdam etc.. ISSN 0021-9991; e-ISSN 1090-2716, more
Peer reviewed article  
Available in  Authors 
Keywords
    Components > Structural components > Grids
    Equations
    Grids
    Motion > Fluid motion > Fluid flow
    Water waves > Gravity waves
    Water waves > Inertial waves
    Waves
    Waves
    Marine/Coastal
Authors  Top 
  • Beckers, J.-M., more
  • Deleersnijder, E., more
Abstract
    The equations governing the propagation of inertia-gravity waves in geophysical fluid flows are discretized on the A, B, C, and D grids according to the classical forward-backward on time and centered on space ( FBTCS) numerical scheme. The van Neumann stability analysis is performed and it is shown that the stability condition of the inertia-gravity waves scheme is more restrictive, at least by a factor of 12, than that concerning pure gravity waves, whatever the magnitude of the Coriolis parameter. Finally, the general necessary and sufficient stability condition is derived for the A, B and C grids, while on the D grid, the stability condition has been obtained only in particular cases.
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