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The time integration is of explicit type
and thus requires strict confirmity of stability criteria for a stable solution. The wellknown CFL condition
for 1D problems is given by
Cr = 1

(5.1) 
with x the mesh width, t the time step, u the flow velocity, and
Cr the Courant number.
For a 2D problem, however, the following CFL condition is employed
A dynamically adjusted time step controlled by the Courant number in a user prescribed range
is implemented in SWASH as follows. The actual
maximum of the Courant number over all wet grid points is determined. The time step
is halved when this number becomes larger than a preset constant
Cr_{max} < 1, and the time step is doubled when this number
is smaller than another constant
Cr_{min}, which is small enough to be sure the time step can be doubled.
Usually,
Cr_{min} is set to 0.2, while the maximum Courant number
Cr_{max} is specified in the range of 0.5 to 0.8. It is advised not to choose a value higher than 0.8 since nonlinear
processes, e.g. wave breaking and wavewave interactions, can affect the stability condition. For high, nonlinear waves, or wave interaction with
structures with steep slopes (e.g. jetties, quays), a Courant number of 0.5 is advised.
Next: Vertical pressure gradient
Up: Numerical parameters
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The SWASH team 20170406