Physically based animation of free surface flows with the Lattice Boltzmann method [Elektronische Ressource] = Physikalische Animation von Strömungen mit freien Oberflächen mit der Lattice-Boltzmann-Methode / vorgelegt von: Nils Thürey

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• Publié par: friedrich-alexander-universitat_erlangen-nurnberg
• Publié le: 01 janvier 2007
• Nombre de lectures: 22
• Langue: English
• Poids de l'ouvrage: 6 Mo

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Physically based Animation of Free Surface
Flows with the Lattice Boltzmann Method
Physikalische Animation von Stro¨mungen mit
freien Oberfla¨chen mit der
Lattice-Boltzmann-Methode
¨ ¨Der Technischen Fakultat der Universtitat Erlangen-Nu¨rnberg,
zur Erlangung des Grades:
Doktor-Ingenieur
Vorgelegt von:
Dipl. Inf. Nils Thu¨rey
Erlangen, 2007AlsDissertationgenehmigtvon
derTechnischenFakulta¨tder
Universita¨tErlangen-Nu¨rnberg
TagderEinreichung: 2006-10-09
TagderPromotion: 2007-03-13
Dekan: Prof.Dr.-Ing.A.Leipertz
Berichterstatter: Prof.Dr.rer.nat.habil.U.Ru¨de
Prof.Dr.M.Pauly
iiAbstract
The numerical simulation of fluids has become an established tool in many engineer-
ing applications. Free surface fluids represent a special case that is important for a
variety of applications. For a free surface simulation, a two phase system, such as air
andwater,isdescribedbyasingle fluidphasewithasharpinterface andcorrespond-
ing boundary conditions. This allows the efficient representation and simulation of
complex problems. In this thesis, the main application for free surface flows will be
the generation of animations of liquids. Additionally, engineering applications from
materialscienceandparticletechnologyareconsidered.
The simulation algorithm of this thesis is based on the lattice Boltzmann method.
This method has been chosen due to the overall computational efficiency of the ba-
sic lattice Boltzmann algorithm, and its ability to deal with complex geometries and
topologies. The basic algorithm isextended to compute the motion of free surfaces in
three dimensions while conserving the overall mass. Adaptive time steps and grids,
in combination with a turbulence model, allow stable and efficient simulations of de-
tailed fluids. In combination with boundary conditions for moving and deforming
objects, the algorithm represents a flexible basis for free surface simulations. Its per-
formanceonsingleCPUmachineswillbeevaluated. Likewise,performanceresultsof
parallelizedversionswillbegivenforshared-anddistributed-memoryarchitectures.
Forfluidsincomputergeneratedanimationsitisimportanttogiveanimatorscon-
trolofthefluidmotion. Anapproachtoperformthisfluidcontrol,withoutdisturbing
thenaturalfluidbehavior,willbegiven. Anothertypicalproblemisthesimulation of
largeopenwatersurfacesduetothehighlydifferingscalesofwavesanddrops. Anex-
planationofhowtoperformsuchsimulationsusingacombinationoftwo-dimensional
and three-dimensional techniques will be given, in combination with a particle based
drop model. To demonstrate the capabilities of the solver that was developed during
theworkonthisthesis,ithasbeenintegratedintoanopensource3Dapplication.
Finally, areas of future work and possible extensions of the algorithm will be dis-
cussed. Oneofthesetopicsistheinclusionofanaccurateandefficientcurvaturecom-
putation for surface tension forces. Furthermore, an outlook of possible applications
inthefieldsofmetalfoamsandcolloidaldispersionswillbediscussed.
iiiivAcknowledgements
First of all I would like to thank my supervisor, Ulrich Ru¨de, for the many helpful
discussions andthe ongoing support – evenwhenmyresearchdrifted awayfrom en-
gineeringapplicationstowardsmorevisuallyorientedtopics. Iamalsogratefultothe
people who helped me writing this thesis by proofreading parts of it: Christian Fe-
ichtinger, Bettina Frohnapfel, Jan Go¨tz, Klaus Iglberger, Thomas Pohl, Stefan Thu¨rey
andBenBergen. EspeciallyBenremovedasignificantamountof”german-english”.
Furthermore, numerous other persons were very helpful during the course of my
work on this thesis. The many discussions with my colleagues Thomas Pohl, Jan
Treibig, Christian Feichtinger and Klaus Iglberger were certainly valuable in many
ways. Likewise Marc Stamminger, Thomas Zeiser, Frank Firsching, Anja Borsdorf,
Gu¨nther Greiner, Quirin Meyer and Vivek Buwa helped by giving me vital hints for
certain aspects of this work. Furthermore, Carolin Ko¨rner and Michael Thies were
veryimportantbydevelopingthefoundationsoftheLBMfreesurfacealgorithm,and
helping me during my master thesis. Together with Thomas Pohl, who agreed to su-
pervisemymaster thesisin2003,theygot mestarted withLBMand the freesurfaces.
Overall, many thanks to my colleagues at the LSS, who, among other things, helped
me getting distracted from all the bugs and instabilities, e.g., by accompanying me
to the Havanna Bar and the E-Werk. Kudos especially to those that did not use my
Mu¨sli-milkfortheircoffee.
Aside from my work at the LSS, the collaboration with ETH Zurich allowed me
to work on one of the most interesting topics of this thesis – the control framework
of Section 9. Mark Pauly and Richard Keiser significantly contributed to this work,
whileMarkusGrossandMarcStammingerhelpedtomakethiscollaborationpossible.
ThanksalsototherestoftheAGG&CGLteamsformakingitaveryenjoyablevisit.
Inaddition,theBlenderdevelopmentandusercommunitywashelpfultestingthe
solver. Some people produced several impressive animations with it. Thanks also
to Bassam Kurdali for providing the rigged character that was used in several test
animationsthroughout theworkonthisthesis.
Finallyand naturally, I wantto thankthe rest of myfamily– myparents Verena &
Stefan,mybrotherArne,mysisterJana,mygrandparentsHannelore,GeorgandMag-
dalena–fortheirencouragingcommentsinthelastthreeyears. Theyhadtoendurea
streamofemailswithstrange fluidtest pictures andbuggy animations(that probably
won’tstopinthenearfuture).
ThisworkhasbeensupportedbytheGraduateCollegeGRK-244,3-DImageAnaly-
sisandSynthesis,oftheGermanScienceFoundation(DFG).
vNomenclature
Note: Especially for parametrization and derivation of the simulation algorithm, all
physical values will be marked with an apostrophe. The majority of the following
equations, however, will use dimensionless lattice quantities. In the following table,
valueswithoutunitsarebydefaultnon-dimensional,unitsareonlygivenforphysical
quantities.
f particledistributionfunctionalonganarbitraryvelocityvectori
f distributionfunctionalongtheinversevelocityvectoroff˜ ii
eqf equilibriumdistributionfunctioni
∗f postcollisiondistributionfunctioni
g particledistributionfunctionforashallowwaterLBMi
w LBequilibriumweightingfactori
m(x) fluidmassofthecellatpositionx
ǫ(x) fillfractionofthecellatpositionx
C Smagorinskyconstant
2P fluidpressure[N/m ]
r domaingridresolution
′S realworlddomainsize[m]
◦T fluidtemperature[ C]
3ρ fluiddensity[kg/m ]
′Δt physicaltimestep[s]
′Δx physicalcellsize[m]
′ dynamicviscosity[mPa/s]
′ 2ν kinematicviscosity[m /s]
λ relaxationtime[s]
Δt latticetimestep
Δx latticecellsize
ν latticeviscosity
τ latticerelaxationtime
E fluidfractiondeviationforaccuracymeasurements
e velocityvectoroftheLBmodeli
T 2g gravityaccelerationvector(0,0,−9.81) [m/s ]
u fluidvelocity[m/s]
n surfacenormalvector
u obstacleobjectvelocity[m/s]o
n obstacleobjectsurfacenormalo
−23 2 −2 −1R Boltzmannconstant1.38065010 [m kgs K ]
Kn Knudsennumber(ratioofmeanfreepathandchar. scale)
Re Reynoldsnumber
γ energy,secondhydrodynamicmoment
ε expansionparametergivenbyKn
viAdditionalnotationfortheLagrangiandropmodel(Section10.3):
m dropmass[kg]P
w dropvelocity[m/s]
w dropvelocityrelativetosurroundingfluid[m/s]rel
F dragforce[N]D
F gravitationalforce[N]G
C dragcoefficientD
Abbreviations
API applicationprogramminginterface
CAD computeraideddesign
D2Q9 two-dimensionalLBmodelwithninevelocities
D3Q19 three-dimensionalLBmodelwithnineteenvelocities
DF distributionfunction(usuallydenotedf )i
BGK BhatnagarGrossKrookapproximationofthecollisionoperator
GUI graphicaluserinterface
LB latticeBoltzmann
LBM latticeBoltzmannmethod
LES largeeddysimulation
MRT multirelaxationtimemodel
MPI distributedmemoryparallelprogrammingAPI
NS Navier-Stokes
OpenMP sharedmemoryparallelprogrammingAPI
SPH smoothedparticlehydrodynamics
SWS shallowwatersimulation
VOF volumeoffluidfreesurfacesimulationmodel
viiviiiContents
1 Introduction 1
2 SimulationofFreeSurfaceFlows 5
2.1 AnimatingFreeSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 ComparingSimulationApproaches . . . . . . . . . . . . . . . . . . . . . 7
3 TheLatticeBoltzmannMethod 11
3.1 HistoricalDevelopment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 TheBasicAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.5 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5.1 TheNavier-StokesEquations . . . . . . . . . . . . . . . . . . . . . 18
3.5.2 TheBoltzmannEquation . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.3 Chapman-EnskogExpansion . . . . . . . . . . . . . . . . . . . . . 21
3.5.4 DerivationoftheLatticeBoltzmannEquation . . . . . . . . . . . 22
3.6 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 LatticeBoltzmannSimulationswithaFreeSurface 27
4.1 InterfaceMovement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 FreeSurfac