Building models to compute the sediment transport in Ca Mau coastal zone

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not contain the K parameter. In this research, we use K tocompute the values of any sediment.

2.3. Algorithm

All of the models use an alternating direction implicit(ADI) finite different method to solve the problems. Themethod involves two stages. In each stage, a tri-diagonal

matrix for the computational domain is built to solve thevalues:

There are millions of nodes to compute the values.There are also millions of equations to be solved. The tri-diagonal matrix method will increase the speed of com-puting because values out of the diagonals are 0. Finite Different Method to solve the sediment

transport model

- The first stage

We have: (2.1)

(2.2)

(2.3)

(2.4)

(2.5) (2.7)

Compute (2.1) by applying (2.2), (2.3), (2.4), (2.5), we

have:

where:

Building the tri-diagonal matrix for the computationaldomain to solve the values.

- The second stage

We have: (2.6)

(2.7)

(2.8)

(2.9)

(2.10)

Compute (2.6) by applying (2.7), (2.8), (2.9), (2.10), we

have:

where:

x

CCuu

x

Cu

t

ji

t

ji

t

ji

t

ji

22

2

1

,12

1

,1

2

1

,2

12

1

,2

1

y

CCvv

y

Cv

t

ji

t

ji

t

ji

t

ji

22

1,1,

2

1

2

1,

2

1

2

1,

x

CCHE

x

CCHE

xH

x

CHE

xH

t

ji

t

jit

jix

t

ji

t

jit

jix

t

ji

x

2

1

,12

1

,2

1

,2

1

2

1

,2

1

,12

1

,2

1

2

1

,

111

y

CCHE

y

CCHE

yH

y

CHE

yH

t

ji

t

jit

jiy

t

ji

t

jit

jiy

t

ji

y

1,,2

1

2

1,

,1,2

1

2

1,

2

1

,

111

2

1

2

1

,12

1

,2

1

,1

t

i

t

jii

t

jii

t

jii dCcCbCa

2

1

,2

1

2

1

,

2

2

1

,2

12

1

,2

11

2*2

t

jix

t

ji

t

ji

t

ji

iHE

Hxx

uu

a

21

,2

121

,2

1

2

1

,

2)(

12 t

jix

t

jix

t

ji

i HEHE

Hxt

b

2

1

,2

1

2

1

,

2

2

1

,2

12

1

,2

11

2*2

t

jix

t

ji

t

ji

t

ji

i HE

Hxx

uu

c

t

ji

t

ji

t

jiy

t

ji

t

ji

t

jiy

t

ji

t

ji

t

ji

t

ji

t

ji

t

ji

t

jit

ji

i

CCHECCHE

Hy

PKCy

CCvv

t

Cd

1,,2

1

2

1,

,1,2

1

2

1,

2

1

,

2

,1,

1,1,

2

1

2

1,

2

1

2

1,

,

1

222

x

CCuu

x

Cu

t

ji

t

ji

t

ji

t

ji

22

2

1

,1

2

1

,1

1

,2

1

1

,2

1

y

CCvv

y

Cv

t

ji

t

ji

t

ji

t

ji

22

1

1,

1

1,

1

2

1,

1

2

1,

x

CCHE

x

CCHE

xHx

CHE

xH

t

ji

t

jit

jix

t

ji

t

jit

jixt

ji

x

2

1

,12

1

,1

,2

1

2

1

,2

1

,11

,2

11

,

111

y

CCHE

y

CCHE

yHy

CHE

yH

t

ji

t

jit

jiy

t

ji

t

jit

jiyt

ji

y

1

1,

1

,1

2

1,

1

,

1

1,1

2

1,1

,

111

11

1,

1

,

1

1,

t

j

t

jij

t

jij

t

jij dCcCbCa

1 11 1, , 112 2

12 ,12 * 22,

t tv vi j i j t

a HEyj i jty y Hi j

b1

c1

a2

b2

c2

a3

b3

c3

ai

bi

ci

aI-1

bI-1

cI-1

aI

bI

x1

n+1

x2

n+1

xI-1

n+1

xI

n+1

x3

n+1

xi

n+1

d1

d2

dI-1

dI

d3

di

. . .

. . ..

.

.

.

.

.

.

.

* =

2

,

2

1

,

t

CC

t

Ct

ji

t

ji

2

2

1

,

1

,

t

CC

t

Ct

ji

t

ji

JOURNAL OF COMPUTING, VOLUME 4, ISSUE 6, JUNE 2012, ISSN (Online) 2151-9617

https://sites.google.com/site/journalofcomputing

WWW.JOURNALOFCOMPUTING.ORG 44


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(2.20)

(2.21)

Building the tri-diagonal matrix for the computationaldomain to solve the values.

Initial conditionsAt time t = 0:u = 0, v = 0, = 0C(x,y,0) = C0(x,y) or C(x,y,0)= constant

Boundary conditions For the current model- Compute tidal components:or- Compute Q = U * WThen, compute the velocities at the boundaries. For the sediment transport model- Solid boundary:

- Liquid boundary:o Water flow runs from outside to the domain:

C = Cb(t)o Water flow runs out of the domain:

Diagram Compute the current

1 12 1

1 12 1 , ,( ) 2 2,

t tb HE HE y yj t i j i jt y Hi j

1 11 1

, , 112 2

12 1 ,2 * 2 2,

t tv vi j i j t

c HEyj t i jy y Hi j

1 11 1 12 21 12 1 1, ,, 1, 1,2 2 2 2

, 1 ,2 2

2

1 1 1 11 1 12 2 2 2

, ,1 11, 1,2 1 , ,2 2,

t t t tt u uC CC i j i j t ti j i j i j

d KC Pj i j i jt x

t t t t t tHE C C HE C Cx xi j i ji j i jt i j i jx H

i j

N

i

iiitA

1

)sin(

0

n

C

02

2

x

C





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Compute the sediment transport Finite different grid

3. Experimental results

Applying the models in Ca Mau coastal zone.The study area (W=61 km; L=88 km) is computed un-

der the following conditions:

Figure 1. Map of the study area

Boundary condition the for current modelOn the open boundary, the water levels are given by

computing tidal components as shown in table I and II.The parameters of these tidal components are from [11,12, 13].Table 1. TIDAL CHARACTERISTICS AT EASTERN SEA

No. Name oftidal com-ponents

Amplitude(m)

Phase(rad)

1 M2 0.72 0.59

2 N2 0.15 0.08

3 S2 0.3 1.3

4 K2 0.08 1.3

5 K1 0.59 5.4

6 O1 0.42 4.6

7 P1 0.19 5.4

8 Q1 0.01 4.2

9 M4 0.01 4.8

10 MS4 0.01 5.8

11 M6 0.004 2.6





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Table 2. TIDAL CHARACTERISTICS AT THAI LAN BAY

No. Name oftidal com-ponents

Amplitude(m)

Phase(rad)

1 M2 0.15 1.35

2 N2 0.15 0.08

3 S2 0.12 1.354 K2 0.08 1.3

5 K1 0.38 0.18

6 O1 0.25 1.8

7 P1 0.49 5.4

8 Q1 0.07 4.2

9 M1 0.08 3.5

Wind: Southern West direction, 4.2m/s. Sediment concentration at boundaries: 0.0001g/ml BOD:Background concentration: 1 mg/lConcentration at boundaries: 1 mg/l DO:Background concentration: 7.0 mg/lConcentration at boundaries: 7.0 mg/l Let K1 = 0.009; K2 = K3 = 0.01

Compute DO

Figure 2. Concentration of DO after 1 month and15 days

Figure 3. Concentration of DO after 1 month, 15days and 6 hours

Figure 4. Concentration of DO after 1 month, 15 days and12 hours





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Compute BOD

Figure 6. Concentration of BOD after 1 month and15 days

Figure 7. Concentration of BOD after 1 month, 15days and 6 hours






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The speed of the modelsThe models run on the computer Core Duo 3GB.

The programming language used to compute the valuesis C#.

myx 300 It takes 160 hours to compute the values for 3 months inreality.

(a) Theory results (a) Results of the modelFigure 10: Sediment transport results(a): after 1hour; (b): after 3 hours; (c): after 5 hours

Evaluate:The results get from the models are similar to the ones

in theory. This prove that the models can be applied toreality.

FUTURE DEVELOPMENTSThe models have been tested in Ca Mau coastal zone.

To be more reliable, the model needs to be tested in realaccidents with enough data.

CONCLUSIONSThis paper presents models to compute the sediment

transport at an estuary. We have built a new algorithmand applied it to the models to get better results than theprevious ones: applying the coefficient K to a generalcase. In addition, the results were tested with simulationexperiments. With the reliability and good speed of com-putation, we can apply the models to reality.

REFERENCES[1] Charles W. Downer, William F. James, Aaron Byrd,and Gregory W. Eggers (2002). Gridded Surface Subsur-face Hydrologic Gridded Surface Subsurface HydrologicAnalysis (GSSHA) Model Simulation of Hydrologic Con-ditions and Restoration Scenarios for the Judicial Ditch 31Watershed, Minnesota.[2] ng Cng Minh, Nguyn Hu Nhn (1993). Thytriu bin ng, chng trnh nghin cu cp nh ncKT. 03, ti KT.03.03.

[3] Eric Wolanski, Nguyen Huu Nhan, Simon Spagnol(1998). Sediment Dynamics During Low Flow Condi-tions in the Mekong River Estuary, Vietnam.[4] Hansen M, DeFries R. (2004). Detecting long termforest change using continuous fields of tree cover mapsfrom 8 km AVHRR data for the years 19821999. Ecosys-tems in press.[5] Hans J. Friedrich (2004). Preliminary results from anumerical multilayer model for the circulation in theNorth Atlantic.[6] Ioannis Tsanis (2006). Environmental Hydraulics -Volume 56: Hydrodynamic and Pollutant Transport

Models of Lakes an Coastal Waters. Elsevier Press.[7] Kiyoshi Horikawa (1988). Nearshore Dynamics andCoastal Processe. University of Tokyo Press.[8] Leo C. Van Rijn (1993). Principles Of SedimentTransport In Rivers Estuaries And Coastal Seas. DelftHydraulics.[9] Le Thi Viet Hoa, Haruyama Shigeko, Nguyen HuuNhan and Tran Thanh Cong (2008). Infrastructure effectson floods in the Mekong River Delta in Vietnam.[10] Nguyen Thi Bay, Nguyen Ky Phung (2002), The 2 -Dmodel of flow and sediment transportation in a curvedopen channel, International colloquium in mechanics ofsolids, fluids, structures and interaction.[11] Phan Vn Hoc, Nguyn Hu Nhn (1993). Nghincu xm nhp mn trn sng ng Nai phc v nh mync 100.000m3/ngy, Tng c Kh tng thy vn, phnvin Kh tng thy vn ti TPHCM.[12] Phan Vn Hoc (2004). Bo co ti: Nghin cutng tc ng lc hc bin sng ven bin Cn Giphcv xy dng c sh tng cho du lch TPHCM, SKhoahc v cng ngh TPHCM.[13] Trung tm kh tng thy vn pha Nam (2000). Vaitr ca thy triu trong vn ngp lt ti TPHCM,TPHCM[14] Usama Saied, I.K. Tsanis (2008). A coastal area

morphodynamics model. Journal of EnvironmentalModelling & Software 23, 35-49.[15] Z.Kowalid (Univ. Alaska), T. S. Murty (Inst. OceanScience B.C) (1993), "Numerical Modeling of Ocean Dy-





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namics", Advanced Serieson Ocean Engineering - Volume5.[16] DHI Software (2007). MIKE 21 Flow Model - Mudtransport module. Scientific Background.




Building models to compute the sediment transport in Ca Mau coastal zone

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