a numerical simulation of coastalhydrodynamics, sedimentation...

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

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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

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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

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Artificial

tidal

zone –

results

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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

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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

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a) Onshore Scenario

Morphological changes after one year

4. Model Applications

2. Khanyounis Fishing Harbour - Proposed

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b) 100m Offshore Scenario

Morphological changes after one year

4. Model Applications

2. Khanyounis Fishing Harbour - Proposed

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c) 200m Offshore Scenario

Morphological changes after one year

4. Model Applications

2. Khanyounis Fishing Harbour - Proposed

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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

34

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

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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

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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