A Numerical Simulation of
Coastal Hydrodynamics, Sedimentation and Salinity
Circulation
Mazen AbualtayefFaculty of Engineering, The Islamic University of Gaza
Modeling and Simulation Mathematical Tools for Civil and Environmental Applications
2
Contents
1. Coastal Numerical Modeling
2. Outline of the Model
3. Model Verification
4. Model Applications
3
1. Coastal Numerical Modeling• utilizes a wide variety of applications to assess
physical processes and environmental impacts relative to proposed improvements to beaches, ports and marine structures.
• allow the simulation of wind, waves, hurricanes, water quality, tides and currents to aid in the development of coastal projects.
• an essential tool in developing a complete understanding of the coastal process at a specific project site.
4
2. Outline of Numerical Model
• 3D multi-layer model• Staggered grid• Shallow water equations with Advection-
diffusion terms• Fractional step method (FDM and Galerkin FEM)• Wind Speed and direction• Wetting and drying algorithm• Salinity and temperature with Advection-
diffusion equations• Beach morphological evolution
5
2.1 Momentum Equations
2
2
2
2
2
21
z
v
y
v
x
v
y
pfu
z
vw
y
vv
x
vu
t
vvh
2
2
2
2
2
21
z
u
y
u
x
u
x
pfv
z
uw
y
uv
x
uu
t
uvh
gdzzgpz
21
z
gdzxx
gx
p2
1 11
z
gdzS 2
gz
p
10
x
yz
z = 0
6
z
SK
zy
S
x
SA
z
Sw
y
Sv
x
Su
t
SCC 2
2
2
2
1000 t32
0 0000389.0001570.04708.1069.0 SSS
1324.011344.0
26.67
0.283
570.503
98.300
2
ttt BA
T
TT
32 100010843.0098185.07869.4 TTTAt
62 1001667.08164.0030.18 TTTBt
2.2 Tracer advection-diffusion equation
State equation of Knudsen
hhvdz
yudz
xt
2.3 Continuity Equation
0
z
w
y
v
x
u
z
h
z
hhz vdz
yudz
xww
z
y
x
(i+1,j+1,k+1)
(i,j,k+1)
(i,j,k)
(i,j+1,k+1)
7
2.6 Staggered grid system
u(i,j,k+1) u(i+1,j,k+1)
u(i,j,k) u(i,j+1,k)F(i,j,k)
F(i,j,k+1)• u, v velocities
are calculated at midway
• w, η, S, T are
calculated at cell face center
The computation domain is divided into positive lattice
8
2.7 Fractional Step Method
xguL
dt
uu
t
u mm
mdm
)(1
STEP1： Discretization in horizontal differentiation FDM
STEP2： Discretization in vertical differentiation FEM
)( 12
1
mdmd
uLdt
uu
t
u
zzzwL v
m 2
yv
xuL mm
1
yyxxhh
9
3.1 Wind-induced circulation
3.2 Tide-induced circulation
3.3 WAD scheme
3.4 Artificial tidal flat with linear slope
3.5 Density currents
3.6 Artificial tidal flat with flat bed
3. Model Verification
10
3.1 Wind-induced circulation
• Basin: 2x2 km x10 m• Non-slip bottom condition• Grid step = 100 m• Time step = 5 s• v = 0.01 m2s-1
• T = 43,200 s • Wind stresses: (a) 0.75, (b)
1.5 Nm-2
• The water depth was divided into 6, 9, and 12 layers
To examine the vertical profile of horizontal velocity
Computation conditions
Computation domain
11
3.1 Wind-induced circulation
• The computed results are almost identical to analytical solutions
• The relative error is decreasing by increasing the number of layers
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
-0.2 -0.1 0 0.1 0.2 0.3 0.4
z (m
)
u (m/sec)
Analytical
6 Layers
9 Layers
12 Layers
(a)
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
-0.2 -0.1 0 0.1 0.2 0.3 0.4
z (m
)
u (m/sec)
Analytical
6 Layers
9 Layers
12 Layers
(b)
0.75 Nm-2
1.5 Nm-2
12
3.2 Tide-induced circulation
• Basin: 2.9x1.4km x10m• Non-slip bottom
condition
• 10 layers • Grid step=100 m• Time step = 5 s• v = 0.01 m2s-1
• Amp = 1.0m• T = 43,200 s
Computation conditions
To examine the horizontal velocity and surface elevation
Computation domain
13
3.2 Tide-induced circulation
-100
-75
-50
-25
0
25
50
75
100
125
150
175
200
0 6 12 18 24
Time (hour)
Analytical surface elevation in cm
Numerical surface elevation in cm
Analytical velocity in mm/sec
Numerical velocity in mm/sec
The water level is agree within 0.1%, and u-velocity is correct within 0.4% with the analytical solution
14
3.6 Artificial tidal zone with flat bed
0
500
1000
1500
2000
2500
3000
0 1000 2000 3000 4000 5000 6000X(m)
0.001m/s
st1 st2 st3 st4
• Nodes: 61×31×6 (vertical) • 5 layers • x =y = 100 m• t = 1 s• T = 43,200 s• h = 50 m2s-1
• v = 0.01 m2s-1
• Kc = 50.0 m2s-1
• Ac = 0.005 m2s-1
• Cf = 0.0026 • T0 = 22.0 ℃• S0 = 0.0 ‰
CASE 1 CASE 2 CASE 3
Amplitude (m) 0.0 1.0 1.0
Density change Yes No Yes
Cases computation conditions
Test Layout, depth is 10 m
Computational conditions
15
Artificial
tidal
zone –
results
16
Computational conditions
Computation Domain
1. Northern Ariake Sea
1 11 21 31 41 51 61 71 81S1
S11
S21
S31
S41
S51
S61
S71
S81
S91
S101
x (i )
y (j )
Nagasu
Miike
SuminoeTakezakijima
Wakatsu
Isahaya bay
Op
en
bou
nd
ary
St.5
St.4
St.3
St.2
St.1
• Nodes: 101×101×6 (vertical) • 5 layers • x = y = 500 m• t = 1.0 s• T = 172,800 s• h = 10 m2s-1
• v = 0.1 m2s-1
• Kc = 10 m2s-1
• Ac = 0.001 m2s-1
• C = 10.0 • a = 1.32 m•• T0 = 15°C • S0 = 30‰
4. Model Applications
17
Water levels
Station name
Computed results Observation*
Amplitude, m
Phase, degree
Amplitude, m
Phase, degree
Nagasu 1.471 258 1.475 N/A
Takesakijima 1.566 259 1.580 259
Miike 1.551 259 1.590 259
Wakatsu 1.617 262 1.610 262
Suminoe 1.725 280 1.721 267
Northern Ariake
bay - results
Amplitudes and phase angles
1 11 21 31 41 51 61 71 81S1
S11
S21
S31
S41
S51
S61
S71
S81
S91
S101
x (i )
y (j )
Nagasu
Miike
SuminoeTakezakijima
Wakatsu
Op
en
bou
nd
ary
St.5
St.4
St.3
St.2
St.1
Amplitudes and phase angles
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
Su
rface e
lev
ati
on
, m
St1 St2 St3 St4 St5
Time, hour
18
Northern
Ariake
Sea
Surface
Salinity &
depth
average
tidal
currents
19
a) Onshore Scenario
Morphological changes after one year
4. Model Applications
2. Khanyounis Fishing Harbour - Proposed
20
b) 100m Offshore Scenario
Morphological changes after one year
4. Model Applications
2. Khanyounis Fishing Harbour - Proposed
21
c) 200m Offshore Scenario
Morphological changes after one year
4. Model Applications
2. Khanyounis Fishing Harbour - Proposed
22
0.2 0.20.4 0.4
0.60.811.21.41.61.822.22.42.62.83
3.23.43.6
3.8
4
4.2
0
0
0
800
600
400
200
0
0 100 200 300 400 500 600
X(m)
Y(m)
Unit: m1m/s
800
600
400
200
0 200 400 600
X(m
)
Y(m)
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
1414
800
600
400
200
0
0 100 200 300 400 500 600
X(m)
Y(m)
Unit: m-1
0
1
2
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5
6
7
8
9
10
11
12
13
1414
5
800
600
400
200
0
0 100 200 300 400 500 600
X(m)
Y(m)
Unit: m
4. Model Applications
3. Gaza Beach Erosion - Detached breakwater
23
0.20.40.60.811.21.41.61.82
2.22.42.62.83
3.23.43.6
3.8
4
4.2
0
0
800
600
400
200
0
0 100 200 300 400 500 600
X(m)
Y(m)
Unit: m1m/s
800
600
400
200
0 200 400 600
X(m
)
Y(m)
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
1414
800
600
400
200
0
0 100 200 300 400 500 600
X(m)
Y(m)
Unit: m -1
012
3
4
5
6
7
8
9
10
11
12
13
1414
800
600
400
200
0
0 100 200 300 400 500 600
X(m)
Y(m)
Unit: m
4. Model Applications
3. Gaza Beach Erosion - Groins
24
4. Model Applications
4. Brine Diffusion for STLV
Seawater Desalination
Plant in Deir Al Balah
25
Surface layer
Bottomlayer
4. Model Applications
4. Brine Diffusion for STLV
Seawater Desalination
Plant in Deir Al Balah
鳥取 26
Thank you for
your attention
