
100
supporting operations through provision of static
guidelines which does not utilize the full dynamic
optimization potential of the port.
In this paper we will introduce a next generation
type physics-based port traffic management system
called NCOS ONLINE. The cloud-based system was
originally presented in Mortensen et al 2016
[5]
and
Mortensen et al 2018
[6]
and is capable of optimizing
port capacity and reduce delays from channel to berth
with the accuracy of 3D full bridge simulators and
using the same numerical framework for both
strategic planning and subsequent operational
decision support. This paper focus on presenting the
underlying equational framework and validation of
the underlying physical response engines and provide
a brief introduction to how they are integrated and
operated through a series of user-friendly web
dashboards.
2 NUMERICAL MODELLING FRAMEWORK
2.1 Vessel Frequency Response
For simulating wave vessel frequency response under
power, NCOS ONLINE uses the 2nd order 3D panel
method engine, S-OMEGA, which is used in the Full
Bridge Simulator SIMFLEX4 by FORCE
TECHNOLOY incorporating implicitly the effect of
vessel forward speed and varying water depths. For
simulating vessel wave frequency response at berth
the numerical solution can be made more
computationally efficient by neglecting forward
speed. For this purpose, NCOS utilizes DHI’s own 3D
frequency radiation-diffraction solver FRC, which is
DHI’s boundary element code used to solve the linear
boundary problem for the free surface flow around a
body to calculate vessel first order wave forces and
second order wave drift forces in the frequency-
domain. Because of its computational efficiency FRC
is capable of fast and accurately modelling a wide
range of typical berth type multibody scenarios such
as caused by reflective quays or tandem moored
vessels.
2.2 Vessel Motion Analysis
NCOS is directly integrated with the phase-averaged
3rd generation wave model MIKE 21 Spectral Wave
model (MIKE 21 SW) and phase resolving models like
MIKE 21 Boussinesq Wave model (MIKE 21 BW) or
the 3D model MIKE 3 Wave FM enabling the accurate
prediction of spatially and temporally varying wave
response through a channel and at berth.
For powered vessel response the frequency
domain wave response is evaluated in the form of 1st
order motion response amplitude operators (RAO’s)
and MIKE 21 SW model provides the wave conditions
along with 2nd order vertical motions (T
(2)
).
The spectral form of the 1st order motions of a
user-specified number of motion points (d) on the
vessel in a specific sea state is calculated from the
motion RAO for the specified point and the sea
spectrum as shown in (1).
2
.
dd
S RAO S
(1)
where
d
AO is the RAO calculated by S-OMEGA
translated to each motion point on the vessel
d
, S
is the wave spectra at each timestep and vessel
position
and
d
S is the resulting motion response
spectra at each motion point
d . Equational
framework for calculating dynamic heel and squat is
presented in Harkin A. et al 2018
[1]
.
The 2
nd
order set down,
2
T
, is calculated from
(2) to (4) where
2
F is the second order
force/moments extracted from S-OMEGA,
is the
wave direction and
C is the restoring force.
2
2
, , ,
F
SFS
(2)
2
2
,
F
Sd
x
C
(3)
222 2
,**
d heave roll y pitch x
Txxdxd
(4)
For moored vessel response NCOS uses its non-
linear dynamic vessel mooring analysis model MIKE
21 MA to calculate vessel motions in the time-domain.
The incident wave potential
I
and first order
dynamic pressure
I
P is evaluated across the 3D
vessel hull from a 2D/3D wave input from MIKE 21
BW/MIKE 3 Wave FM or a surface evaluation time
series synthesized from MIKE 21 SW. The first order
radiation velocity potential
is computed by FRC.
The wave exciting force
jD
Ft is then calculated
from the Haskind relations:
,.
,,
b
b
jD I j
S
jIn
S
Ft Pxtnxdx
txdxd
∬
∬
(5)
Subsequently the equation of motion for the
moored vessel is evaluated in the time domain using
Equation 2.
¨
0
1,2,...,
t
N
k
jk jk jk k jk k
k
jD jnl
MxtKtxdCxt
Ft Ft j N
(6)
Second order wave drift forces are calculated
using the far field approximation method presented
in Newman J. N. (1974)
[2]
. Wind and current forcing
are accounted for as either spatially uniform (0D) or
spatially varying (2D) data files using vessel specific
drag coefficients. Mooring line and fender forces are
calculated based on actual load-displacement curves.
Viscous damping is included as a combination of
constant friction damping plus linear, quadratic and
cubic damping.