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The maximum time step one can take is set by the assumption that one
can consider each cell only to interact with its direct neighbours:
the domain of influence of cell should not reach cells and
! Since the maximum communication speed is or , this
gives a condition on the time step. This is known as the *Courant-Friedrichs-Lewy (CFL) condition*. If your time step exceeds
this value, the method will become unstable. Since this maximum time
step depends on and , this means that the time step is not
fixed, but depends on the conditions on the grid, and should be
re-calculated every time step. It is normally wise to take a fraction
between 1 and 0.5 of this maximum time step.

Garrelt Mellema
2003-01-20