MIKE 21 BW - Discretisation of the Convective Terms

Reference Manual
120 MIKE 21 BW - © DHI
Discretisation of the convective terms
Default settings
As default the 2DH Boussinesq equations are solved by implicit finite differ-
ence techniques with variable defined on a space-staggered rectangular grid.
The convective terms are discretized using central differences and the nor-
mal ADI algorithm with 'side-feeding' is used for numerical integration. The
'side-feeding' technique (see e.g. Abbott and Minns, 1998, p 314ff) is intro-
duced to centre the cross-momentum derivatives (the so-called cross-terms)
without numerical dissipation.
Alternative schemes
In applications with large gradients in the convective terms the default
approach may results in numerical instabilities and eventually model blow-
up. Those applications are characterised by having high spatial resolution
(e.g. dx= dy= 1-2 m) and large incident short period waves. To circumvent
instabilities alternative discretisation methods of the convective terms have
been implemented:
 central differencing with simple upwinding at steep gradients and near
land
 quadratic upwinding with simple upwinding at steep gradients and near
land
 simple upwinding differencing
All three schemes are characterised by having some numerical dissipation,
which may damp possible instabilities. The simple upwind scheme is the
most dissipative scheme. The dissipation is in general much less than the
damping caused by using backward time centring of the cross-terms.
Recommendations
If instability occurs it is recommended to first apply the “Central differencing
with simple upwinding at steep gradients and near land”. In case of a blow-up
you can try the quadratic upwinding scheme. If the instability still persists
please try the simple upwind scheme.
Please notice that the CPS (Computational Points per Second) is lower for
the upwind schemes than using central differences and the normal ADI algo-
rithm with “side-feeding”. The CPS is typically reduced by a factor of 0.5-0.8.
For stability reasons it is recommended to use the scheme ‘Simple upwinding
at steep gradients and near land’ for the space discretisation of the convec-
tive terms in connection with simulations including wave breaking (and mov-
ing shoreline).