Fast and accurate front propagation for simulation of geological folds

84 Pages·2013·22.81 MB·English

Fast and accurate front propagation for
simulation of geological folds
by
Tor Gillberg
Thesis submitted for the degree of Philosophiae Doctor
Department of Informatics
Faculty of Mathematics and Natural Sciences
University of Oslo
October 2013

Preface
Early2010IreceivedanindustrialPhDscholarshipwithKalkuloAS,acommercialsubsidiaryofthe
SimulaResearchLaboratory. DuringmytimewithKalkulo,IhavebeenpartoftheCompoundEarth
Simulatordevelopmentteam. CompoundisStatoiltechnologyinwhichmodelsoftheinnerearthare
transformedbetweendifferentstructuralstates. Thesetransformationsareusedrepeatedly,andmust
beperformedfastinorderforthesoftwaretobeuserfriendly. Thisthesissummarisesmyresearchon
numericalaspectsoftheCompoundEarthSimulator.
IwouldliketothankmysupervisorsAreMagnusBruaset,ChristianTarrou,AslakTveitoandmy
informalbutactingsupervisorØyvindHjelle. ThroughoutmytimeatSimula,AreMagnusBruaset
has helped steer my research towards useful and interesting subjects. His scientific understanding
andhelphasbeeninvaluable. AspartofKalkulo,Ihaveparticipatedinseveralinterestingmeetings
withkeypersonnelinStatoilincludingthevisionaryCompoundtechnologyleaderSteenA.Petersen.
ThemathematicalmodelandnumericalframeworkofCompoundwasdevelopedbyØyvindHjelleat
Kalkulo. Hjelle’sworkhasbeenthebaseofmyresearch,andhisdetailedunderstandingandinterest
hasbeenusefulandencouraging.
Simulaprovidesafriendlyandwelcomingenvironmentformanytalentedresearchersandgood
friends. Answerstomanyquestionshaveoftenbeenfoundintheofficenextdoor,andIamthankfulfor
thehelpfromMohammedSourouri,TanguiMorvan,Omaral-Khayatandseveralothercolleaguesat
Simula. Myfamilyhavebeensupportivethroughoutmywork,thankyouallforbeingsounderstanding.
Finally,noneofmyresearchwouldeverhavebeencompletedwithouttheunderstandingandsupport
fromHelena,thankyou.
III

Contents
Preface iii
ListofPapers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Introduction 1
1 TheCompoundEarthSimulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Motivationofresearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Frontpropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 Foldsimulationsbyfrontpropagations . . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Solutionalgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
6 Researchpapers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
PaperI:Accuracyandefficiencyofstencilsfortheeikonalequationinearthmodelling 19
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Finitedifferencestencils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Diagonalstencilforimprovedaccuracy . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Numericaltests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
PaperII:Asemi-orderedfastiterativemethod(SOFI)formonotonefrontpropagationin
simulationsofgeologicalfolding 49
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3 Frontpropagationalgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Thesemi-orderedfastiterativemethod . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Numericalverification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
PaperIII:Anewparallel3Dfrontpropagationalgorithmforfastsimulationofgeological
folds 61
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2 The3DParallelMarchingMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A Conditionalupwindapproximations . . . . . . . . . . . . . . . . . . . . . . . . . . 70
PaperIV:ParallelsolversforstaticHamilton-Jacobiequationsinthreedimensions 75
1 Computerbasedmodellingofgeology . . . . . . . . . . . . . . . . . . . . . . . . . 78
V
2 StaticHamilton-Jacobiequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3 Developingfastparallelsolvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4 Numericalverification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5 Simulatinggeologicalfolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A Efficientformulationoftheeikonal“pyramid”stencil . . . . . . . . . . . . . . . . . 117
B Subdomains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
C Implementationdetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
List of Papers
PaperI
•
Accuracyandefficiencyofstencilsfortheeikonalequationinearthmodelling
TorGillberg,ØyvindHjelle,AreMagnusBruaset
PublishedinComputationalGeosciences16,number4(2012),pages933-952.
PaperII
•
A semi-ordered fast iterative method (SOFI) for monotone front propagation in simula-
tionsofgeologicalfolding
TorGillberg
PublishedintheproceedingsofMODSIM2011,19thInternationalCongressonModellingand
Simulation,pages641-647.
PaperIII
•
Anewparallel3Dfrontpropagationalgorithmforfastsimulationofgeologicalfolds
TorGillberg,MohammedSourouri,XingCai
PublishedinProcediaComputerScience,9,pages947-955. ProceedingsoftheInternational
ConferenceonComputationalScience,ICCS2012.
PaperIV
•
ParallelsolversforstaticHamilton-Jacobiequationsinthreedimensions
TorGillberg,AreMagnusBruaset,MohammedSourouri,ØyvindHjelle
SimulaTechnicalReport,July2013. Underpreparationforjournalpublication.
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