Adaptive mesh refinement applied to tsunami modeling: TsunaFLASH [Elektronische Ressource] / Widodo Setiyo Pranowo

Widodo Setiyo Pranowo

Description

Adaptive Mesh Refinement Applied to Tsunami Modeling: TsunaFLASHWidodo Setiyo PranowoA dissertation submitted in partial fulfillment ofthe requirements for the degree of doctor in engineering (Dr. Ing)Supervisors:1. Prof. Dr. Wolgang Hiller (Alfred Wegener Institute)2. Prof. Dr. Jorn¨ Behrens (Universitat¨ Hamburg)Submitted on June 28, 2010Colloquium on July 29, 2010Program Authorized to Offer Degree: Fachbereich 3 Mathematik und Informatik,Universitat¨ Bremen2010AbstractAdaptive Mesh Refinement Applied to Tsunami Modeling: TsunaFLASHWidodo Setiyo PranowoThe devastating Sumatra-Andaman tsunami of December 2004, is a milestone for the internationalcommunity striving to introduce measures to prevent hazards from (future) tsunamis. One of themeasures is numerical modeling which plays a key role for predictions as well as inundation map-ping developments.Numerical modeling has been used as a tool for analyzing and reconstructing tsunamis foralmost 40 years. Nowadays, many tsunami codes are available as open-source or free-ware andwidely used in the tsunami modeling community. Many numerical methods have been applied suchas finite difference, finite element and finite volume. The same applies to gridding methods, such asstructured and unstructured non-adaptive types.This thesis introduces a new triangle-based adaptive mesh finite element model for tsunamipropagation (and inundation) simulations.

Sujets

• Mathematics

Informations

• Publié par: universitat_bremen
• Publié le: 01 janvier 2010
• Nombre de lectures: 70
• Poids de l'ouvrage: 31 Mo

Extrait

AdaptiveMeshRefinementAppliedtoTsunamiModeling:TsunaFLASH

WidodoSetiyoPranowo

Adissertationsubmittedinpartialfulfillmentof
therequirementsforthedegreeofdoctorinengineering(Dr.Ing)

Supervisors:1.Prof.Dr.WolgangHiller(AlfredWegenerInstitute)
2.Prof.Dr.J¨ornBehrens(Universit¨atHamburg)

201028,JuneonSubmitted

201029,JulyonColloquium

ProgramAuthorizedtoOfferDegree:Fachbereich3MathematikundInformatik,
Universit¨atBremen
2010

Abstract

AdaptiveMeshRefinementAppliedtoTsunamiModeling:TsunaFLASH

WidodoSetiyoPranowo

ThedevastatingSumatra-AndamantsunamiofDecember2004,isamilestonefortheinternational
communitystrivingtointroducemeasurestopreventhazardsfrom(future)tsunamis.Oneofthe
measuresisnumericalmodelingwhichplaysakeyroleforpredictionsaswellasinundationmap-
elopments.vdeping

Numericalmodelinghasbeenusedasatoolforanalyzingandreconstructingtsunamisfor
almost40years.Nowadays,manytsunamicodesareavailableasopen-sourceorfree-wareand
widelyusedinthetsunamimodelingcommunity.Manynumericalmethodshavebeenappliedsuch
asfinitedifference,finiteelementandfinitevolume.Thesameappliestogriddingmethods,suchas
structuredandunstructurednon-adaptivetypes.

Thisthesisintroducesanewtriangle-basedadaptivemeshfiniteelementmodelfortsunami
propagation(andinundation)simulations.TsunaFLASHcombinesanumericalmethoddevelopedin
theframeworkoftheunstructuredtriangularelement,yetnon-adaptive,tsunamimodelTsunAWI
withadaptivemeshrefinementcapabilitiesprovidedbythelibraryamatos.Themethodsarewell
suitedforaccurateresolutionoflocalizedfeatures,maintainingcomputationalefficiencyintermsof
thenumberofcomputationsandtherequiredmemory.

InthisfirstdevelopmentsofTsunaFLASH,anumberofexperimentshavebeenperformedfor
testing.Thereare:Anexperimentsonvariousinitialconditions,fromananalyticalsourceuptoa
couplingtothesophisticatedrupturegeneratorRuptGen;experimentswithdiverseerrorestimators
fortestingrefinementcriteriaandadaptationalgorithms;benchmarkexperimentsusinganalytical
solutionsandfieldobservationswheretheanalyticalsolutionisderivedfromthefirstbenchmark
problemfromTheInternationalLongWavesreference;andtheseasurfaceelevationinthefielddata
experimentisusedfromthesatellitetracksofJason-1andTopexforverificationoftheSumatra-
Andamanmega-tsunami2004event,whilethewaterlevelreadingofDART23401isusedforthe

verificationoftheAndamanminortsunami2009.

Someadditionalstudieshavebeenconductedtoassessthephysicalbackgroundoftsunamis

simulationandtestpropersupportingtoolsforTsunaFLASH.Thereexperimentscomprisesource

modelreconstructionsandsimulationsbasedupontheseinthecontextofaprobableworstcase

tsunamisimulationforPadang;experimentstotesttheinfluenceofdifferenttypesoftopographies

ontheinundationbehavior;andaninvestigationofthemostrepresentativesourcemodelforthe

Andaman-Sumatramega-tsunamiof2004.Finally,theambiguityofthearrivaltimeoftheJava

minortsunami2009isexperimentallyinvestigated.

Keywords:tsunami,numericalmodel,finiteelement,unstructuredmesh,adaptivemesh

Zusammenfassung

AdaptiveGitterVerfeinerungangewandtaufdieTsunamiModellierung:TsunaFLASH

DerverheerendeSumatra-Andamanen-TsunamivomDezember2004isteinMeilensteinf¨ur
dieinternationaleGemeinschaftbeiderErgreifungvonMaßnahmen,Gefahrenzuk¨unftigerTsunamis
zureduzieren.F¨urdieVorhersagevonAnkunftszeitenderWellenunddieEntwicklungvon¨Uberflungs-
kartenspieltnumerischeModellierungeineSchl¨usselrolle.
NumerischeModellierungwirdseitfast40JahrenzurAnalyseundRekonstruktionvon
Tsunamisverwendet.VieleTsunami-CodessindOpenSourceoderFreewareundweitverbreitet
inderTsunami-Modellierungsgemeinschaft.VerschiedenenumerischeMethodenwerdenange-
wandt,wiez.B.dieFinite-Differenzen-,dieFinite-Elemente-oderdieFinite-Volumen-Methode.
BeiderGittergenerierungwirdzwischenstrukturiertenundunstrukturiertensowienichtadaptiven
undadaptivenVerfahrenunterschieden.
IndieserArbeitwirdeinneuesFinite-Elemente-ModellzurBerechnungderAusbreitungs-
und¨UberflutungsphasevonTsunamiwelleneingef¨uhrt,welchesaufadaptiverGitterverfeinerung
basiert.TsunaFLASHverbindetdasVerfahrenderadaptivenGitterverfeinerung(mitHilfederBib-
liothekamatos)mitdemnichtadaptivenFinite-Elemente-ModellTsunAWI.BeideMethodensind
f¨ureinehoheAufl¨osunglokalerGegebenheitensehrgeeignet,wobeidienumerischeEffizienzin
BezugaufdieAnzahlderBerechnungenunddenben¨otigtenSpeicherplatzerhaltenbleibt.
IndererstenEntwicklungsphasevonTsunaFLASHwurdenzahlreicheUntersuchungendurch-
gef¨uhrt:UnterschiedlicheAnfangsbedingungenwurdengetestet,voneineranalytischenQuellebis
zueinerkomplexenDeformationdesMeeresbodens(generiertdurchdasProgrammRuptGen).
VerschiedeneFehlersch¨atzerf¨urVerfeinerungskriterienundAlgorithmenzuradaptivenGitterver-
feinerungwurdenverglichen.BenchmarkexperimentemitanalytischenL¨osungenundFelddaten
wurdendurchgef¨uhrt.DieanalytischeL¨osungistvomerstenBenchmarkproblemderInternational
LongWaves-Konferenzabgeleitet.ZurValidierungdesModellswurdenSatellitentracksvonJason-
1undTopex,welcheDatenderMeeresspiegelauslenkungdesSumatra-Andamanen-Megatsunamis
von2004lieferten,verwendet.DerWasserstandderBojeDART23401dientederValidierungder

ModellergebnissedeskleinerenAndamanen-Tsunamisvon2009.

Zus¨atzlicheStudienwurdendurchgef¨uhrt,umdenphysikalischenHintergrundvonTsunami-

simulationenzuuntersuchensowiediekorrekteFunktionsweisederunterst¨utzendenWerkzeugef¨ur

TsunaFLASHzutesten:ZumeinenbeinhaltendieseExperimenteRekonstruktionenvonAnfangsbe-

dingungenundSimulationenimKontexteinesm¨oglichenworst-case-TsunamisvorPadang,Suma-

tra.DabeiwurdederEinflussvonverschiedenenTopographiedatens¨atzenaufdas¨Uberflutungs-

verhaltenuntersucht.Zumanderenwurdedasammeistenrepr¨asentativeQuellmodellf¨urden

Andamanen-Sumatra-Megatsunamiermittelt.SchließlichwurdendieUnklarheitenbeiderBes-

timmungderAnkunftszeitendesJava-Tsunamisvon2009n¨aherbetrachtet.

Stichw¨orter:Tsunami,numerischesModell,Finite-Elemente-Methode,unstrukturiertesGit-

ter,adaptivesGitter.

CONTENTSOFABLET

ListofFigures..........................................

ListofTables..........................................

Glossary.............................................

Chapter1:Introduction..................................
1.1Tsunamiintheworld.................................
1.2TsunamiModeling..................................
1.3Motivationandobjective...............................
1.4Thesisoverview....................................

Chapter2:TheModel..................................
2.1Shallowwaterequation................................
2.2Unstructuredfiniteelementmethod..........................
2.3Leapfrogscheme...................................
2.4Inundationboundarycondition............................
2.5Manningsroughnessandviscosity..........................

Chapter3:AdaptiveMeshRefinement..........................
3.1amatos........................................
3.2Meshrefinementandcoarsening...........................
3.3Spacefillingcurve..................................

Chapter4:NumericalDevelopment...........................
4.1Spatialdiscretization.................................
4.2Timedescritization..................................
4.2.1Physicalandnumerical(wave)mode....................
4.2.2Robert-Asselintimefilter...........................
4.3Timestepcontrol...................................

i

ageP

vi

ix

x

12578

101011121212

15151717

212123242626

4.4Inundationscheme..................................
4.5Bottomfriction....................................
4.6Smagorinskyhorizontalviscosityterm........................

Chapter5:Tools.....................................
5.1Visualizationtools..................................
5.1.1tsunaflashplot.m.............................
5.1.2tsunaflashmovie.m............................
5.1.3rgb2bmp.sh.................................
5.2Analysisandverificationtools............................
5.2.1tsunamifft.m................................
5.2.2tsunamimagnitude.m...........................
5.2.3tsunaflashtseries.m...........................
5.2.4tsunaflashcomparerunupbeach.m...................
5.2.5tsunaflashcomparesattrack.m.....................
5.3SeaBottomDeformationGenerator.........................
5.3.1tsunamirupdimslip.m...........................
5.3.2SeaBottomDeform.f90..........................
5.3.3tsunamiprojection.m...........................
5.4Initialgridgeneratorforscenarioofrunupinachannel...............

Chapter6:Modelsetup,NumericalExperimentResultsandDiscussion........
6.1Modelsetup......................................
6.1.1Bathymetryandtopography.........................
6.1.2Initialcoarsemesh..............................
6.1.3Hardwareandsoftware............................
6.2Experimentonthediverseinitialconditions.....................
6.2.1Cosinebell..................................
6.2.2Ellipticsource................................
6.2.3Couplingwitharupturegenerator......................
6.2.4Faultparameters...............................
6.3Experimentonthediverseerrorestimators......................
6.4Bechmark:Runuponaslopingbeach........................
6.5Experimentonthediverseadaptationalgorithm...................
6.6Computationalspeed................................