MIKE 21 BW - Courant number

Reference Manual
178 MIKE 21 BW - © DHI
5.5.6 Courant number
The Courant Number is an expression which describes the number of grid
points that wave information will travel in one time step. It is defined as fol-
lows:
(5.14)
where c is the wave propagation speed (or celerity), t is the time step, and
x is the spatial resolution.
Important: The Courant number should always be equal to, or less than, 1 in
2D applications and less than about 0.5 in 1D applications.
5.5.7 Deep water terms
MIKE 21 BW solves the classical form and an enhanced form of the Boussin-
esq equations. The enhanced equations are different from the classical for-
mulation as a number of new Boussinesq correction terms (so-called deep
water terms) are included.
The major restriction of the classical form of the Boussinesq equations is the
shallow water limitation in terms of the water depth to deep water wave length
ratio, h/L
0
. Celerity errors gradually increase for increasing h/L
0
, and 5% is
reached for h/L
0
= 0.22, which is often taken as the practical deep water limit
for these equations.
The new form of the Boussinesq equations incorporates a significant
improvement of the dispersion relations, which makes it possible to use the
new equations to simulate the propagation of irregular wave trains in shallow
to deep water up to a depth to deep water wave length ratio, h/L
0
, of 0.5.
5.5.8 First time model set-up
For an efficient determination of the model resolution in space and time you
can use the MIKE 21 BW Model Setup Planner.
Alternatively you can follow the short recipe listed below. The procedure is for
typical short period wave disturbance study using unidirectional or directional
waves.
Cr c
t
x
-------
=