Lattice Boltzmann Method of a Flooding Accident at Gopeng...

Research ArticleLattice Boltzmann Method of a Flooding Accident at GopengPerak Malaysia

Siti Habibah Shafiai Diana Bazila Shahruzzaman Goh Juin Xien andMohamed Latheef

Department of Civil and Environmental Engineering Universiti Teknologi PETRONAS 32610 Bandar Seri Iskandar Perak Malaysia

Correspondence should be addressed to Siti Habibah Shafiai sitihabibahshafiaiutpedumy

Received 20 April 2017 Accepted 31 May 2017 Published 16 August 2017

Academic Editor Jian G Zhou

Copyright copy 2017 Siti Habibah Shafiai et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The extraordinary flood had hit the residential area at Taman Raia Mesra Gopeng Perak Malaysia in November 2016 The eventillustrated how the river basin had been fully inundated due to the heavy rainfall and caused the overflow to this affected area Itwas reported that the occurrence became worst as the outlet of retention pond which connects to the river is unsuitable for thewater outflow Henceforth this paper attempts to evaluate the causal factor of this recent disaster by using a model developed fromLattice Boltzmann Method (LBM) The model also incorporated with the rainfall and stormwater in LABSWE The simulationwas commenced with the basic tests for model validation comprising turbulent and jet-forced flow in a circular channel whichresulted in a good agreement for both models The simulation continued by using LABSWE model to reveal the water depth andvelocity profile at the study site These results had proven the incompatibility size of the outlet pond which is too small for thewater to flow out to the river The study is capable of providing the authorities with a sustainable design of proper drainage systemespecially in Malaysia which is constantly receiving the outrageous heavy rainfall

1 Introduction

A flood is well defined as the overflow of high water fromthe occupied water basin system including river and stream[1] Flood is ranked as a third largest of the disastrous eventsamong the Asian countries after wave surge and wind storm[2] The occurrence can be dangerous to life and can lead toeconomic and properties loss In Malaysia a flood is not anew occasion especially for those who settled at the northeastof Peninsular Malaysia Generally the area will be floodedduring northeast monsoon season held betweenOctober andMarch almost every year

Perak which is located nearby the northeast state ofPeninsular Malaysia is not exempted from the flood attacksIn December 2014 the state of Perak was affected by theastonishing flood on a scale that has never been experiencedbefore It is reported that more than 50 relief centres havebeen operated due to this event with Perak Tengah as themost affected district Typically the cause of flood is a heavycontinuous rainfall however the major triggering factor forthe flood is the improper drainage system [3] Yoon et al

(2010) investigated that almost 30of the flood is contributedby the improper setup of a drainage system followed bypollution and urbanization management with 20 and 18respectively [3] The flood can affect onersquos life (death) andhealth including psychological or physiological problems[4]

Recognizing the adverse consequence of the flood thereis a need to demonstrate such a natural phenomenon byusing a model or device that provides an accurate predictionThe Computational Fluid Dynamics (CFD) model appliedin the water sector is a prevailing device to simulate thecondition of the fluid especially in urban hydrology andwater management field [5] The ability to investigate thereal situation by using a device can help to predict thefuture condition [6] Hence we benefit by comparing andimprovising both theory and the real-life situations Thereare numerous numbers of computer models for simulatingthe water sector including WEST SIMBA and MIKE Theevolution in technology enables the researchers to study theirscope up to themicroscopic scale and today it is even possibleto formulate the complex system

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 3478158 10 pageshttpsdoiorg10115520173478158

2 Mathematical Problems in Engineering

Lattice Boltzmann Method (LBM) is a modern com-puter model using High-Performance Computing (HPC)efficiently for fluid simulation within the complex geometries[7] LBM is an advanced technique evolved from the LatticeGas Automata (LGA) method LGA method represents themacroscopic physical variables meanwhile LBM is able tosolve the flow problem up to the microscopic equation [8]LBM is proposed to allow an easy program and can be usedfor simulating the complex flow in complex geometries TheLBM comprised three criteria including lattice Boltzmannequation lattice pattern and local equilibrium distributionfunction These tasks are responsible for forming a latticeBoltzmann equation for shallow water flows known as LAB-SWE

The LABSWE had been applied in various conditions ofwater flow by many scientists including steady and unsteadyflows tidal flows and turbulent flows in different dimensions[7] The findings were compared with the physical modellingor analytical solutions in order to demonstrate their valida-tion The result shows that the accuracy of the LABSWE isvery promising hence proving the efficiency and capabilitiesof the method in simulating fluids

The flood study by using the numerical approached hadbeen explored by many researchers [9 10] However thesestudies focus on the scope of macroscopic result only Onthe other hand the study on flood is by using the LABSWEproviding a microscopic outcome The research may involveseveral variables including river profile water flow directionand water depth profile which help to estimate the futureoccurrence of the flood hence reducing the risk of flood [11]

Taman Raia Mesra located at Gopeng Perak is underconstruction for the residential area The project site is about30 acres of land with the presence of retention pond locatednearby the housing area The retention pond is attached withthe adjacent river by an outlet In November 2016 the areawas flooded which caused a major loss to the developer Thearea received about 821mm rainfall intensity throughout theevent The continuous heavy rainfall is causing the waterfrom the nearby river Sg Tekah to overflow at the site It ismentioned that the housing area was inundated by flood forabout three days The ground visit observed that one of thefactors that may cause the flood is the size of outlet drainageof the retention pond which is too small

The study was then started immediately after the event toovercome the problem The LABSWE is used in this studyto analyse the flood at Taman Raia Mesra The model alsoincorporates in the LABSWE the rainfall and stormwaterparameters that lead to the flood The few basic tests wereinvestigated for themodel validation including turbulent flowand jet-forced flow in a circular channel The simulationresults of the study area are capable of providing the author-ities with a sustainable design of proper drainage system atTaman Raia Mesra Gopeng Perak hence preventing theoccurrence of a future flood at the site

2 Materials and Methods

21 Lattice Boltzmann Model for Shallow Water Equationwith Turbulent Flow (LABSWE) The LBM for shallow water

1

234

5

6 7 8Figure 1 Lattice pattern with a 9-velocity square [12]

equation (LABSWE) based on the 9-velocity square latticepattern is approached The lattice pattern indicated themovement of the particle on a lattice unit at its velocity alongone of the eight links specified 1ndash8 (Figure 1) Meanwhile thezero value means the particle is at resting phase with zerospeed

TheLattice Boltzmann equation (LBE) can be determinedas

1198911015840119886 (119909 + 119890120572Δ119905 119905 + Δ119905) = 119891120572 (119909 119905) + Δ1199051198731205721198902 119890119886119894119865119894 (119909 119905) (1)

where 119891119886 is the particle distribution function 119890 = Δ119909Δ119905whereΔ119909 is the lattice size andΔ119905 is the time119873120572 is a constantdetermined by

119873120572 = 11198902sum120572 119890119886119909119890119886119909 =

11198902sum120572 119890119886119910119890119886119910 (2)

There are two steps in LBM including streaming andcollision If the particles move at their own velocities towardstheir nearest neighbours it is called streaming step On theother hand collision step occurs when the particles arriveat lattice point and have interaction with one another Thisinteraction according to the scattering rules will affect theirvelocities and directionHence the new distribution functionis expressed as

119891120572 (119909 119905) = 1198911015840120572 (119909 119905) minus Ω120572 [1198911015840120572 (119909 119905) minus 119891eq120572 (119909 119905)] (3)

where Ω120572 is the collision operator and 119891eq119886 is the local equi-

libriumdistributions functionThe combination of streamingand collision steps in a 9-velocity square lattice modified thelattice Boltzmann equation as

119891119886 (119909 + 119890120572Δ119905 119905 + Δ119905) = 119891120572 (119909 119905)minus 1120591119905 [119891120572 (119909 119905) minus 119891

eq120572 (119909 119905)]

+ Δ11990561198902 119890120572119894119865119894

(4)

Mathematical Problems in Engineering 3

where 120591119905 is the total relaxation time for modelling flowturbulence and can be calculated from

120591119905 = 120591 + 1205911198901015840

120591119890 =minus120591radic1205912 + 181198622119878 (1198902ℎ)radicΠ119894119895Π119894119895

2 (5)

In the equation above 120591119890 is the eddy relaxation time and Π119894119895is defined as

Π119894119895 = sum120572

119890120572119894119890120572119895 (119891120572 minus 119891eq120572 ) (6)

In order to identify the velocity vector of particles in thesquare lattice the equation that follows will be approached

119890120572

=

(0 0) 120572 = 0119890 [cos (120572 minus 1) 1205874 sin (120572 minus 1) 1205874 ] 120572 = 1 3 5 7radic2119890 [cos (120572 minus 1) 1205874 sin (120572 minus 1) 1205874 ] 120572 = 2 4 6 8

(7)

Hence to solve the shallow water equations using LBM alocal equilibrium function is defined as

119891eq120572 =

ℎ minus 5119892ℎ261198902 minus 2ℎ

31198902 119906119894119906119894 120572 = 0119892ℎ261198902 minus

ℎ31198902 119890120572119894119906119894 +

ℎ21198904 119890120572119894119890120572119895119906119894119906119895 minus

ℎ61198902 119906119894119906119894 120572 = 1 3 5 7

119892ℎ2241198902 minus

ℎ121198902 119890120572119894119906119894 +

ℎ81198904 119890120572119894119890120572119895119906119894119906119895 minus

ℎ241198902 119906119894119906119894 120572 = 2 4 6 8

(8)

where ℎ is water depth and 119906119894 is flow velocity which can beobtained through

ℎ = sum120572

119891120572

119906119894 = 1ℎsum120572 119890120572119894119891120572

(9)

22 Flood Model There are a few parameters taken intoaccount for the flood model in this study The dischargerainfall (119876) was focusing on the data on November 2016 withthe catchment area located in a nearby city Ipoh is takenas a reference The discharge can be calculated by using theRational Formula based on urban Stormwater ManagementManual for Malaysia (MSMA 2)

119876 = 119862 times 119894 times 119860360 (10)

where 119876 is a peak flow (m3s) 119894 is the average intensity ofrainfall and119860 is site area119862 is the coefficient of a rainfall thatcan be obtained from the table provided by MSMA 2

The discharge of a domestic waste usage is derived fromthe continuity equation

119876 = 119860119881 (11)

where 119876 is a peak flow (m3s) 119860 is an average intensity ofrainfall and 119881 is the water velocity The velocity of the waterflow is obtained by using Manningrsquos equation

119881 = 11198991198772311987812 (12)

In (12) 119881 is defined as the velocity of water in the drain(ms) 119899 is Manningrsquos Roughness coefficient obtained from

the MSMA 2 119877 (m) is referred as a hydraulic radius and 119878(mmhr) is a drain slope

For the simulation process the inlet drainage to the riveris set up with a rectangular channel with dimension andslope of 300mm times 600mm and 119878119886 = 0002 respectivelyMeanwhile the river nearby is defined to be rectangularstream channel with a flatbed bathymetry The layout planof the river is developed by integrating the AutoCAD systeminto LABSWE

3 Results and Discussion

31 Turbulent Flow within a Channel with a Circular CavityThe flow in a channel with a circular cavity is simulatedto demonstrate the ability of the model in simulating theeffect of the turbulent flow in a river attached to a lake[12] The shape of the model prediction for the simulationis prepared as illustrated in Figure 2 The model is designedwith a rectangular channel 189m wide and 189m long Thechannel is attached to a circular sidewall cavity on the rightside of the channel with a radius of 315m

The simulation is set up to a constant value of flowvelocitycomponents 119906 = 025ms and V = 0ms The water depth ismaintained at ℎ = 025m A 190 times 70 lattice with grid spaceof Δ119909 = 01m applied A semislip boundary condition has asurface roughness coefficient 119862119891 = 00045 and is used at thesolid wallsThe relaxation time and Smagorinsky constant areapplied with 120591 = 06 and 119862119878 = 03 respectively A time stepof Δ119905 = 003 s is applied in this model

The model reached its steady state after 10000th iterationwith relative error 119864119877 = 524 times 10minus9 The fully convergenceflow of velocity vectors and streamlines are generated inthe cavity by the model as illustrated in Figures 3 and 4respectively


315 m

189m

a

a

b b

189 m

Figure 2 Dimension of the open channel with circular sidewall cavity [12]

7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)

Figure 3 Velocity vectors in the circular sidewall cavity [12]

7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)

Figure 4 Streamlines flow in the circular sidewall cavity [12]

The 119906 and V velocity components along the vertical (a-a) and horizontal (b-b) cross section were validated (Figures5 and 6) by comparing the data with data from Kuipers andVreugdenhill (1973) [13] The evaluation demonstrates thatthe model used in this study generates a better outcome thanthe previous data

32 Turbulent Jet-Forced Flow in Circular Basin The jet-forced flow in the circular basin was simulated by using theLABSWE [12]Themodel of the simulation is designed in thesymmetrical shape which is a standard profile of the circularbasinThe dimensions and flow parameters for the model areshown in Figure 7

The simulation flow is prepared with the radius of a basin119903 = 10m with an opening of inlet and outlet is at an angle of12058716 rad The outlet position is separated by 71205878 rad fromthe inlet The model is utilized with 280 times 160 lattice gridspacing Δ119909 = Δ119910 = 00125m with time step Δ119905 = 000625 sFor boundary conditions there is a similar set up at upstreamand downstream channelThemodel is arranged with a waterdepth of ℎ = 01m and velocity components of 119906 = 01ms andV = 0ms

The simulations of the turbulent jet-forced flow showthat the model reached a steady state condition at 10000thiteration with a relative error 119864119877 = 154times10minus7The optimumstreamline with the required circulation length and pattern


7

6

5

3

4

2

1

0

y(m

)

minus01 0 01 02 03

u (ms)

Velocity distribution at a-a

Kuipers and Vreugdenhill model (1973)LB Model

Experimental data Kuipers and Vreugdenhill (1973)

cross section

Figure 5 Velocity components 119906 at the vertical (a-a) cross section [12]

7

6

5

3

4

2

1

0

y(m

)

minus01 0

Velocity distribution at b-b



cross section

minus005 005 01

(ms)

Figure 6 Velocity components V at the horizontal (b-b) cross section [12]


075

m

0156m 15Inlet Outlet

075m 075m 075m 075m

Figure 7 Dimension of the jet-forced flow for the symmetrical circular basin [12]

Figure 8 Velocity vectors of jet-forced flow in the symmetrical circular basin [12]

Figure 9 Streamline contours of jet-forced flow in the symmetrical circular basin [12]

is obtained from 120591 = 055 and 119862119878 = 025 The symmetricalchannel model also generated velocity vectors of eddy andwell-developed circulation flows as illustrated in Figures 8and 9 respectively

The validation is done by comparing the LBM data withthe numerical result by Barberrsquos model Figure 10 shows thevelocity component 119906 profile across the mid-section forLBM and Barberrsquos model It is suggested that the LBM and


0

05

10

15

0 01 02 03 04 05 06 07 08

Numerical result (Barber (1990))LBM

minus01minus02

uua

y(m

)

Figure 10 Comparison of LBM and numerical result in a circular basin [12]

Taman Raia Mesra Gopeng

(c)

(b)

(a)

Figure 11 Location of the case study Taman Raia Mesra Gopeng Perak (a) Map showing the location of the study area in Perak Malaysia(b) Project plan at the study area (c) Retention pond attached with the nearby river at the site

the boundary-fitted primitive variable scheme results are ingood agreement especially in the recirculation zones

33 Case Study Flood at Taman Raia Mesra Gopeng PerakMalaysia Taman Raia Mesra Gopeng is located at the

district of Kampar Perak within a Peninsular Malaysia(Figure 11) This 30-acre land is a project site for the resi-dential area The area was flooded at the end of 2016 andis believed to occur due to the overflow of water from thenearby river basinThe retention pond found nearby the area


River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P

(300 m width)Outlet P

m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ

(600 m amp 700 m width)

60m

60m

12m 6Ｇ

1 500

Figure 12 Cross section of the layout

Sungai Tekah

Outlet pond

River upstream

River downstream

Inlet river300 mm (width)

300 mm (width)

12 m

Figure 13 Data input for simulation showing the outlet of the pond to the river

is a function to hold the excess water from the land and isattached to the river by a small outlet

The cross section layout for the focusing area includinga pond outlet pond and river is illustrated in Figure 12The 60m pond is attached with a drainage 1 as inlet pondand drainage 2 as outlet pond and inlet river in unison Insimulation test the inlet pond is set up with a peak flow of119876 = 00036m3s the height of ℎ119889 = 0025m and velocity inthe 119909 direction of 119906 = 05ms Meanwhile both outlet pond

and inlet river are arranged with119876 = 074m3s ℎ119863 = 0011mand 119906 = 05m The simulation was done in a domain area of635m times 307m

The LABSWE model is used to investigate the behaviourof the water flow The simulation test was carried out byusing a model resulted from a conversion of AutoCAD fileinto PNG image comprising a grid lattice size of 396 times 154(Figure 13) The time step used is 119889119905 = 001 with an iterationof 10000 The kinematic viscosity is set up with 120591 = 11 and119889119909 = 10


0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations

Water depth at pond outlet for time = 100 Ｍ

Figure 14 Water depth at an outlet of the pond at 100 s

50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis

100 ＭContour of water depth (m) at

Figure 15 Contour of water depth at the domain area for 100 s

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis

100 Ｍ (Scale 1 3)Velocity vectors for full domain at

Figure 16 Velocity vectors for a whole domain area at 100 s with the scale of 1 3

The simulation results were observed for every 5 secondsstarting from 0 s up to 100 s The analysis revealed the waterdepth at the outlet of the pond and velocity profile of thedomain area as plotted in Figures 14ndash18

The water depth at the outlet of the pond has beenrecorded for 100 secThe result shown in Figure 14 illustratedthat the water depth in the outlet increased from 09m until092m There are no significant changes of water profileobserved during the simulation However it is noticed thata hydraulic jump profile had occurred within the channelThe occurrence can be related to a steep slope and highvelocity

Figure 15 shows a contour of water depth in the domainarea The highest water depth is observed at the beginningof the channel due to the very steep slope for the outlet Thewater depthwill increasewith time due to the size of the outletchannel that is too small for capturing the water flow

In order to understand the flow directions in the domainarea the figure of velocity vectors has been produced asshown in Figures 16 and 17 Figure 16 is the velocity vectorsfor the whole domain area It is observed that there are noanomalies in the simulation result However a close-up viewhas been done near to the outlet pond area such as in Figure 17shows that the water is flooding from the river into the outlet


60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis

Velocity vectors at pond outlet for 100 Ｍ

Figure 17 Velocity vectors for the outlet pond at 100 s

50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis

Velocity contour at 100 Ｍ

Figure 18 Velocity contour of water flow at 100 s

pond channel This is a very significant effect that can causeflooding to the residential area

In addition towards the results analysis a velocity con-tour of the domain area has been produced and studied asillustrated in Figure 18 The water velocity in the stream hasincreased from 05ms to 109ms due to the heavy rainfallevent

4 Conclusions

The LABSWE is used for simulating a flood event at TamanRaia Mesra Gopeng Perak The turbulent flow and jet forceflow in a circular channel had been tested for a modelvalidation The outcome for both validations shows a verysatisfactory result The LABSWE also has been incorporatedwith rainfall and stormwater parameters for November 2016The investigation had proven the incompatibility of the sizeof the outlet pond which is too small for the water to flow outto the river The situation then can cause a flood to the pondarea and will finally overflow to the residential area In orderto overcome this problem equatorial countries like Malaysiashould consider the heavy rainfall and stormwater dischargewhen designing an outlet as the country is always receivingthe heavy rainfall continuously

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors appreciate the full support by research grantfromMOSTI Science fund (04-02-13-SF0022) It is a pleasureto also acknowledge the Centre of Postgraduate Studiesand Department of Civil and Environmental EngineeringUniversiti Teknologi PETRONAS for their support andencouragement

References

[1] S G Diya M E Gazim M E Toriman and M G AbdullahildquoFloods in Malaysia historical reviews causes effects andmitigations approachrdquo International Journal of InterdisciplinaryResearch and Innovations pp 59ndash65 2014

[2] WMO ldquoRole of WMO and national meteorological and hydro-logical services in disaster risk reductionrdquoWorldMeteorologicalOrganization 2009

[3] K Y Yoon N A Bahrun and Y Kum A study on the urbanflooding Universiti Malaysia Pahang Pahang Malaysia 2010

[4] S N Jonkman and I Kelman ldquoAn analysis of the causes andcircumstances of flood disaster deathsrdquo Disasters vol 29 no 1pp 75ndash95 2005

[5] J Janssen andRMayer ldquoComputational fluid dynamics (CFD)-based droplet size estimates in emulsification equipmentrdquoProcesses vol 4 no 4 pp 1ndash14 2016

[6] D Bigoni A P Engsig-Karup and C Eskilsson ldquoEfficientuncertainty quantification of a fully nonlinear and dispersivewater wave model with random inputsrdquo Journal of EngineeringMathematics vol 101 pp 87ndash113 2016

[7] J G Zhou Lattice BoltzmannMethods for ShallowWater FlowsSpringer Heidelberg Germany 2004

[8] S H Shafiai ldquoA lattice Boltzmann model for the 2D solitarywave run-up around a conical islandrdquo in Proceedings of theCoasts Marine Structures and Breakwaters pp 1ndash10 EdinburghUK September 2013

[9] M Delphi M M Shooshtari and H H Zadeh ldquoApplication ofdiffusion wave method for flood routing in Karun riverrdquo Inter-national Journal of Environmental Science and Development pp432ndash434 2010

[10] A AMahessar A L Qureshi and A Baloch ldquoNumerical studyon flood routing in Indus riverrdquo International Water TechnologyJournal pp 3ndash12 2013

[11] N Liu J Feng and J Zhu ldquoFlood routing based on diffusionwave equation using lattice Boltzmann methodrdquo Procedia Engi-neering vol 28 pp 190ndash195 2012

[12] S H Shafiai Lattice Boltzmann Method for Simulating ShallowFree Surface Flows involving Wetting and Drying [PhD disser-tation] Liverpool University Liverpool UK 2011

[13] J Kuipers and C B Vreugdenhil ldquoCalculations of two-dimensional horizontal flowrdquo Hydraulics Laboratory ReportDelft The Netherlands 1973

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Stochastic AnalysisInternational Journal of


Lattice Boltzmann Method (LBM) is a modern com-puter model using High-Performance Computing (HPC)efficiently for fluid simulation within the complex geometries[7] LBM is an advanced technique evolved from the LatticeGas Automata (LGA) method LGA method represents themacroscopic physical variables meanwhile LBM is able tosolve the flow problem up to the microscopic equation [8]LBM is proposed to allow an easy program and can be usedfor simulating the complex flow in complex geometries TheLBM comprised three criteria including lattice Boltzmannequation lattice pattern and local equilibrium distributionfunction These tasks are responsible for forming a latticeBoltzmann equation for shallow water flows known as LAB-SWE

The LABSWE had been applied in various conditions ofwater flow by many scientists including steady and unsteadyflows tidal flows and turbulent flows in different dimensions[7] The findings were compared with the physical modellingor analytical solutions in order to demonstrate their valida-tion The result shows that the accuracy of the LABSWE isvery promising hence proving the efficiency and capabilitiesof the method in simulating fluids

The flood study by using the numerical approached hadbeen explored by many researchers [9 10] However thesestudies focus on the scope of macroscopic result only Onthe other hand the study on flood is by using the LABSWEproviding a microscopic outcome The research may involveseveral variables including river profile water flow directionand water depth profile which help to estimate the futureoccurrence of the flood hence reducing the risk of flood [11]

Taman Raia Mesra located at Gopeng Perak is underconstruction for the residential area The project site is about30 acres of land with the presence of retention pond locatednearby the housing area The retention pond is attached withthe adjacent river by an outlet In November 2016 the areawas flooded which caused a major loss to the developer Thearea received about 821mm rainfall intensity throughout theevent The continuous heavy rainfall is causing the waterfrom the nearby river Sg Tekah to overflow at the site It ismentioned that the housing area was inundated by flood forabout three days The ground visit observed that one of thefactors that may cause the flood is the size of outlet drainageof the retention pond which is too small

The study was then started immediately after the event toovercome the problem The LABSWE is used in this studyto analyse the flood at Taman Raia Mesra The model alsoincorporates in the LABSWE the rainfall and stormwaterparameters that lead to the flood The few basic tests wereinvestigated for themodel validation including turbulent flowand jet-forced flow in a circular channel The simulationresults of the study area are capable of providing the author-ities with a sustainable design of proper drainage system atTaman Raia Mesra Gopeng Perak hence preventing theoccurrence of a future flood at the site

2 Materials and Methods

21 Lattice Boltzmann Model for Shallow Water Equationwith Turbulent Flow (LABSWE) The LBM for shallow water

1

234

5

6 7 8Figure 1 Lattice pattern with a 9-velocity square [12]

equation (LABSWE) based on the 9-velocity square latticepattern is approached The lattice pattern indicated themovement of the particle on a lattice unit at its velocity alongone of the eight links specified 1ndash8 (Figure 1) Meanwhile thezero value means the particle is at resting phase with zerospeed

TheLattice Boltzmann equation (LBE) can be determinedas

1198911015840119886 (119909 + 119890120572Δ119905 119905 + Δ119905) = 119891120572 (119909 119905) + Δ1199051198731205721198902 119890119886119894119865119894 (119909 119905) (1)

where 119891119886 is the particle distribution function 119890 = Δ119909Δ119905whereΔ119909 is the lattice size andΔ119905 is the time119873120572 is a constantdetermined by

119873120572 = 11198902sum120572 119890119886119909119890119886119909 =

11198902sum120572 119890119886119910119890119886119910 (2)

There are two steps in LBM including streaming andcollision If the particles move at their own velocities towardstheir nearest neighbours it is called streaming step On theother hand collision step occurs when the particles arriveat lattice point and have interaction with one another Thisinteraction according to the scattering rules will affect theirvelocities and directionHence the new distribution functionis expressed as

119891120572 (119909 119905) = 1198911015840120572 (119909 119905) minus Ω120572 [1198911015840120572 (119909 119905) minus 119891eq120572 (119909 119905)] (3)

where Ω120572 is the collision operator and 119891eq119886 is the local equi-

libriumdistributions functionThe combination of streamingand collision steps in a 9-velocity square lattice modified thelattice Boltzmann equation as

119891119886 (119909 + 119890120572Δ119905 119905 + Δ119905) = 119891120572 (119909 119905)minus 1120591119905 [119891120572 (119909 119905) minus 119891

eq120572 (119909 119905)]

+ Δ11990561198902 119890120572119894119865119894

(4)



120591119905 = 120591 + 1205911198901015840


2 (5)


Π119894119895 = sum120572

119890120572119894119890120572119895 (119891120572 minus 119891eq120572 ) (6)


119890120572

=


(7)


119891eq120572 =

ℎ minus 5119892ℎ261198902 minus 2ℎ

31198902 119906119894119906119894 120572 = 0119892ℎ261198902 minus

ℎ31198902 119890120572119894119906119894 +

ℎ21198904 119890120572119894119890120572119895119906119894119906119895 minus

ℎ61198902 119906119894119906119894 120572 = 1 3 5 7

119892ℎ2241198902 minus

ℎ121198902 119890120572119894119906119894 +

ℎ81198904 119890120572119894119890120572119895119906119894119906119895 minus

ℎ241198902 119906119894119906119894 120572 = 2 4 6 8

(8)


ℎ = sum120572

119891120572

119906119894 = 1ℎsum120572 119890120572119894119891120572

(9)


119876 = 119862 times 119894 times 119860360 (10)



119876 = 119860119881 (11)


119881 = 11198991198772311987812 (12)









315 m

189m

a

a

b b

189 m


7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)


7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)







7

6

5

3

4

2

1

0

y(m

)

minus01 0 01 02 03

u (ms)




cross section


7

6

5

3

4

2

1

0

y(m

)

minus01 0




cross section

minus005 005 01

(ms)



075

m


075m 075m 075m 075m







0

05

10

15

0 01 02 03 04 05 06 07 08


minus01minus02

uua

y(m

)



(c)

(b)

(a)






River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






120591119905 = 120591 + 1205911198901015840


2 (5)


Π119894119895 = sum120572

119890120572119894119890120572119895 (119891120572 minus 119891eq120572 ) (6)


119890120572

=


(7)


119891eq120572 =

ℎ minus 5119892ℎ261198902 minus 2ℎ

31198902 119906119894119906119894 120572 = 0119892ℎ261198902 minus

ℎ31198902 119890120572119894119906119894 +

ℎ21198904 119890120572119894119890120572119895119906119894119906119895 minus

ℎ61198902 119906119894119906119894 120572 = 1 3 5 7

119892ℎ2241198902 minus

ℎ121198902 119890120572119894119906119894 +

ℎ81198904 119890120572119894119890120572119895119906119894119906119895 minus

ℎ241198902 119906119894119906119894 120572 = 2 4 6 8

(8)


ℎ = sum120572

119891120572

119906119894 = 1ℎsum120572 119890120572119894119891120572

(9)


119876 = 119862 times 119894 times 119860360 (10)



119876 = 119860119881 (11)


119881 = 11198991198772311987812 (12)









315 m

189m

a

a

b b

189 m


7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)


7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)







7

6

5

3

4

2

1

0

y(m

)

minus01 0 01 02 03

u (ms)




cross section


7

6

5

3

4

2

1

0

y(m

)

minus01 0




cross section

minus005 005 01

(ms)



075

m


075m 075m 075m 075m







0

05

10

15

0 01 02 03 04 05 06 07 08


minus01minus02

uua

y(m

)



(c)

(b)

(a)






River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





315 m

189m

a

a

b b

189 m


7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)


7

6

5

3

4

2

1

02 4 6 8 10 12 14 16 18

x (m)

y(m

)







7

6

5

3

4

2

1

0

y(m

)

minus01 0 01 02 03

u (ms)




cross section


7

6

5

3

4

2

1

0

y(m

)

minus01 0




cross section

minus005 005 01

(ms)



075

m


075m 075m 075m 075m







0

05

10

15

0 01 02 03 04 05 06 07 08


minus01minus02

uua

y(m

)



(c)

(b)

(a)






River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





7

6

5

3

4

2

1

0

y(m

)

minus01 0 01 02 03

u (ms)




cross section


7

6

5

3

4

2

1

0

y(m

)

minus01 0




cross section

minus005 005 01

(ms)



075

m


075m 075m 075m 075m







0

05

10

15

0 01 02 03 04 05 06 07 08


minus01minus02

uua

y(m

)



(c)

(b)

(a)






River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





075

m


075m 075m 075m 075m







0

05

10

15

0 01 02 03 04 05 06 07 08


minus01minus02

uua

y(m

)



(c)

(b)

(a)






River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0

05

10

15

0 01 02 03 04 05 06 07 08


minus01minus02

uua

y(m

)



(c)

(b)

(a)






River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





River

Pond

Drainage 2

Drainage 1

ℎR = 1Ｇ

ℎR2 = 003 Ｇ

Inlet R

Inlet R

Inlet P


m=01666

ℎ D=00

11Ｇ

ℎS = 1Ｇ

ℎP = 1Ｇ

ℎD = 0025 Ｇ


60m

60m

12m 6Ｇ

1 500


Sungai Tekah

Outlet pond

River upstream

River downstream


300 mm (width)

12 m







0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0924

0922

092

0918

0916

0914

0912

091

0908

0906W

ater

dep

th (m

)0 2000 4000 6000 8000 10000 12000

Iterations



50 100 150 200 250

20

40

60

80

100

120

140

05

1

15

2

25

Latti

ces a

ty-a

xis

Lattices at x-axis



0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

Latti

ces a

ty-a

xis

Lattices at x-axis








60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





60 65 70 75 80 8505

1015202530354045

Latti

ces a

ty-a

xis

Lattices at x-axis



50 100 150 200 250

20

40

60

80

100

120

140

00102030405060708091

Latti

ces a

ty-a

xis

Lattices at x-axis





4 Conclusions




Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Lattice Boltzmann Method of a Flooding Accident at Gopeng...

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Transcript of Lattice Boltzmann Method of a Flooding Accident at Gopeng...