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4 CONCLUSIONS
A new fully discrete mass– and total-energy–
conserving finite difference model for the simulation
of shallow-water flows in bay-like domains with com-
plex boundaries was developed. Having taken the
SWEs written in the divergent form, we involved the
idea of operator splitting coupled with the Crank-
Nicolson approximation and constructed absolutely
stable second-order finite difference schemes that al-
low accurate simulation of shallow-water flows in
spherical domains of arbitrary shapes. An important
integral invariant of motion of the SWEs, the potential
enstrophy, proved to be bounded for an inviscid un-
forced fluid, oscillating in time within a narrow range.
Hence, the numerical solution is mathematically ac-
curate and provides physically adequate results. Due
to the method of splitting the developed model can
straightforwardly be implemented for distributed sim-
ulation of shallow-water flows on high-performance
parallel computers. Numerical experiments with a
simple inviscidunforced closed shallow-watersystem
and with a viscous open wind-driven shallow-water
model simulating a real situation nicely confirmed the
skills of the new method.
ACKNOWLEDGEMENTS
This research was partially supported by the grants
No. 14539 and No. 26073 of the National Sys-
tem of Researchers of Mexico (SNI), and is part of
the projects PAPIIT-UNAM IN104811 and PAPIME-
UNAM PE103311, Mexico.
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