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Figure 9.1:
Comparison of the oscillatory response of AdamsBashforth scheme.

The thirdorder AdamsBashforth time stepping (AB3) provides
several advantages (see, e.g., Durran [1991]) compared to
the default quasisecond order AdamsBashforth (AB2):
 higher accuracy;
 stable with a longer timestep;
 no additional computation (just requires the storage of one additional
time level).
The
order AdamsBashforth can be used to
extrapolate forward in time the tendency
(replacing equation 2.24)
which writes:

(9.1) 
The 3rd order AB is obtained
with
.
Note that selecting
one recovers the quasi2nd order AB.
The AB3 time stepping improves the stability limit
for an oscillatory problem like advection or Coriolis.
As seen from Fig.9.1,
it remains stable up to a CFL of 0.72,
compared to only 0.50 with AB2 and
.
It is interesting to note that the stability limit can be further
extended up to a CFL of 0.786 for an oscillatory problem
(see fig.9.1)
using
but then the scheme is only 2nd order accurate.
Figure 9.2:
Comparison of the damping (diffusion like) response of AdamsBashforth schemes.

However, the behavior of the AB3 for a damping problem (like diffusion)
is less favorable, since the stability limit is reduced to
0.54 only (and 0.64 with
) compared to 1. (and 0.9
with
) with the AB2 (see fig.9.2).
A way to enable the use of a longer time step is
to keep the dissipation terms outside the AB extrapolation
(setting momDissip_In_AB=.FALSE. in main parameter file
"data", namelist PARM03),
thus returning to a simple forward timestepping for dissipation,
and to use AB3 only for advection and Coriolis terms.
The AB3 time stepping is activated by defining the option
#define ALLOW_ADAMSBASHFORTH_3
in "CPP_OPTIONS.h".
The parameters
can be set from the
main parameter file "data" (namelist PARM03) and their
default value corresponds to the 3rd order AdamsBashforth.
A simple example is provided in "verification/advect_xy/input.ab3_c4".
The AB3 is not yet available for
the vertical momentum equation (NonHydrostatic)
neither for passive tracers.
Next: 9.1.2 Timeextrapolation of tracer
Up: 9.1 Other Timestepping Options
Previous: 9.1 Other Timestepping Options
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Massachusetts Institute of Technology 
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