OpenFOAMq OpensourceCFDtoolbox,which

suppliespreconfiguredsolvers,utilities andlibraries.

q FlexiblesetofefficientC++modules---object-oriented.

q UseFinite-VolumeMethod(FVM)tosolvesystemsofPDEsascribedonany3Dunstructured meshofpolyhedralcells.

q Goodparallelization. Overview of OpenFOAM structures

q Resourcefulcommunity (CFDforum,http://www.cfd-online.com/Forums/openfoam/)contribution(user-definedlibraries).

q interFoam,whichisasolverfor2incompressiblefluidswithinterfacetracking,isusedinthepresentstudy.Tutorials:http://cfd.direct/openfoam/user-guide/dambreak/

0whereboundaryconditions aredefinedforalpha.water,B,k,nuSgs,p_rgh,U

constant

system

Meshbuilding -- blockMeshDict

Turbulence closure– turbulenceProperties,LESProperties

Computational timecontrol-- controlDict

Numerical schemes -- fvSchemes

Numerical solvers-- fvSolution

Initialcondition -- setFieldslDict

Domaindecomposition -- decomposeParDict

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

x

y

z

0 (00-0.3)

1 (18.200.064)

2 (18.200.3)

Howtochooseanappropriatedomainheight?- Bigenoughtomakesurethebreakingwavewillnottouchthetopboundary;- Nottobig,tosavecomputationalcost.

3 (000.3)

4 (00.6 -0.3)

5 (18.2 0.60.064)

6 (18.20.60.3)

7 (00.60.3)

Howtochooseanappropriatedomainwidth?- Bigenoughtocoverseverallargesteddiesintheexperiment;- Nottobig,tosavecomputationalcost.

Inthiscase,thedomainlengthissettobesmallerthanthatintheexperiment[Ting2006,2008]butlongenoughtocovertheinitialshorelineandswashzone

DomainLayout

Nz=80.Howtodeterminethenumberofgridsintheverticaldirection?-- Determined bythenumberofgridsneededtosolvethewave.

E.g.,inthiscase,H0=0.22m.Using30gridstosolvethewave∆z =7.5mmattheleftboundaryNz =Domainheight/∆z =80

z

Nx=2427.Howtodeterminethenumberofgridsinthestreamwise direction?--Makesuretheratioof∆𝑥/∆𝑧 isnottoobig(<5).

E.g.,inthiscase,Dzmax=7.5mmattheleftboundary;Dzmin=3mmattherightboundary.Tomake∆𝑥/∆𝑧 <5,chooseDxmax=11.5mm(∆𝑥/∆𝑧=3.8)attheleftboundaryandDxmin=4.6mm (∆𝑥/∆𝑧 =1.5)attherightboundary.∆𝑥 isshrinkingfromthelefttotheright.(Sois∆𝑧 )

Buildthegrids

Ny=80.Howtodeterminethenumberofgridsinthespanwisedirection?Makesuretheratiosof∆𝑦/∆𝑧 and∆𝑥/∆𝑦 arenottoobig.E.g.,inthiscase,∆y =7.5mm

x

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Choose theturbulenceclosure

Large-eddysimulation inthissimulation

DynamicSmagorinsky closure isused,andanimprovedversionofdynamicSmagorinsky closuredeveloped byAlbertoPassalacqua isadopted.

HowtoinstalltheimproveddynamicSmagorinsky closureinOpenFOAM?1. Downloadthesourcecodeusinggit:

git clonegit://github.com/AlbertoPa/dynamicSmagorinsky.git2.Enterthedirectorywherethesourcecodehasbeenextracted,andcompileitbytyping:

wmake libso3.AddthefollowinglinetothecontrolDict ofyourcase:libs("libOpenFOAM.so""libdynamicSmagorinskyModel.so");4.SpecifyLESModel dynamicSmagorinsky;deltacubeRootVol;inLESModel.5.Addthesubdictionary

dynamicSmagorinskyCoeffs{filtersimple;ce 1.048;}

toLESModels.

Filter isdefinedas Δ = Vcell3

https://github.com/AlbertoPa/dynamicSmagorinsky

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Settheinitial condition

(00-0.3)

(00.6-0.3)

(000) (00.60)

(150.60)(1500)

Offshore

Onshore

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Definetheboundaries

(Wall function isused)

Sends inthetargetsolitarywavethroughgroovyBC

WhatisgroovyBC?-- Alibrarythatcanbeusedtogeneratearbitraryboundaryconditions basedonexpressions. Itisincluded intheswak4Foamlibrarypackage.

Link:https://openfoamwiki.net/index.php/Contrib/swak4Foam

InstallgroovyBC

1.Downloadswak4Foamlibrarypackagefrom

svn checkoutsvn://svn.code.sf.net/p/openfoam-extend/svn/trunk/Breeder_2.0/libraries/swak4Foam/ swak4Foam_2.x

2.Inthedirectoryofthesources,type

wmake all

UsegroovyBC tosendinsolitarywave

ExpressionofthetheoreticalsurfaceelevationinLeeetal.[1982]

ExpressionofthetheoreticalvelocityinLeeetal.[1982]

α1 =

1, z ≤ Hcosh2 atp −ct + xs( )( )

0, z > Hcosh2 atp −ct + xs( )( )

#

$

%%

&

%%

c = gh 1+H h( )h = 0.3m H = 0.22m fs = 2.644 g = 0,0,−9.81( ) xs = hfsH h

atp = 0.75Hh3

u =

ghHcosh2 atp −ct + xs( )"# $%h

1− 0.25Hcosh2 atp −ct + xs( )"# $%h

"

#&&

$

%'', z ≤ H

cosh2 atp −ct + xs( )( )

0, z > Hcosh2 atp −ct + xs( )( )

)

*

++

,

++

w =

− ghzh

1− 0.5Hdexcosh2 atp −ct + xs( )"# $%h

"

#&&

$

%'', z ≤ H

cosh2 atp −ct + xs( )( )

0, z > Hcosh2 atp −ct + xs( )( )

)

*

++

,

++

v = 0

Specifytheboundary conditions

p_rgh:dynamicpressure

U:velocity

alpha.water: (percentageofwaterineachcell) intheVOFequationα1

B:subgrid-scale tensor inLES.istheunittensor; isthedeviatoric partofthesubgrid-scale tensorandisparameterizedbysubgrid closure

B = 2 3kI +Beff I

k:subgrid-scale kineticenergyinLES.,,istherateofstrain

k = cIΔ2 D 2 cI ≈ 0.2 D

nuSgs:,sub-gridscale viscosity inLESν sgs

Specifytheboundary conditions

zeroGradient:normalgradientiszero

cyclic:periodic boundarycondition

inletOutlet:≈ zeroGradient.ButswitchtofixedValue (using“inletValue”) ifthevelocityjustoutside theboundaryisflowingintothedomain

pressureInletOutletVelocity: =pressureInletVelocity +inletOutpressureInletVelocity: When𝑝 isknownattheinlet,𝑈 isevaluatedfromthefluxnormaltothepath.

totalPressure: Totalpressure is fixed;whenchanges,pwillbeadjustedaccordingly

p0 = p+1 2ρ U2

U

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Numerical schemes

ddtSchemes: firsttime derivative 𝜕/𝜕𝑡 .“CrankNicholson 1”isthepure2nd-orderCrank-Nicolson scheme

gradSchemes: Gradient𝛻.“Gausslinear”meansGauss’theoremisusedwhentransformingintegralovervolumeintointegraloversurface;“linear”meanscentraldifferencescheme (CDS)

divSchemes: Divergent𝛻 ..“GausslimitedLinearV 1”and“GaussvanLeer”arebothTVDschemeswithdifferentlimiters. “Gauss interfaceCompression” isusedfortheinterfacecompression term

interpolationSchemes: numericalscheme fortheevaluation offacevaluesfromthecellcentervalues

snGradSchemes: component ofgradientnormaltoacell face

fluxRequired: fieldswhichrequirethegeneration ofaflux

laplacianSchemes: Laplacian .“Gauss linearcorrected”isCDSwithsomecorrectionterms

∇2

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Numerical solvers

SolvesthePressurePoissonEquation

Setthesolversforp_rgh andU

PIMPLE=SIMPLE+PISO

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Setthetimecontrol

startFrom

stopAt

deltaT

writeControl

adjustTimeStep

maxCo

maxAlphaCo

maxDeltaT

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Decompose thedomain

“decomposeParDict”

simpleCoeffs{n(412);…

}

numberOfSubdomains 8;

x

y

z

TypedecomposePar

Buildthedomainandsetthegrids

Choosetheturbulence closure

Setthe initial condition

Settheboundarycondition

Choosethenumericalschemes

Choosethenumericalsolvers

Setthetimecontrol

Decompose thedomain

Runthecase

Runthecase

TypeinterFoam