LEWASTE Users Manual.docx
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LEWASTE Users Manual.docx
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LEWASTEUsersManual
LEWASTE.DOC{PRIVATE}
Users'ManualofAHybridLagrangian-Eulerian
FiniteElementModelofWASTETransport
throughSaturated-UnsaturatedMedia:
Version2.0
by
G.T.(George)YehandJ.R.(Ruth)Chang
DepartmentofCivilEngineering
ThePennsylvaniaStateUniversity
UniversityPark,PA16802
DateIssued-May1993
PreparedfortheShortCourseon
SimulationofSubsurfaceFlowandContaminantTransport
byFiniteElementandAnalyticalMethods
CONTENTS
Page
LISTOFFIGURESv
LISTOFTABLESvii
ABSTRACTix
1.INTRODUCTION1
2.THELEWASTEPROGRAMSTRUCTURE3
2.1PurposeofLEWASTE3
2.2DescriptionofLEWASTESubroutines6
3.ADAPTATIONOFLEWASTETOSITESPECIFICAPPLICATIONS25
3.1SpecificationofMaximumControl-Integers25
3.2InputandOutputDevices29
4.SAMPLEPROBLEMS31
4.1StatementofProblemNo.131
4.2InputforProblemNo.135
4.3PartialOutputforProblemNo.135
4.4StatementofProblemNo.243
4.5InputforProblemNo.246
4.6PartialOutputforProblemNo.246
4.7StatementofProblemNo.355
4.8InputforProblemNo.361
4.9PartialOutputforProblemNo.361
APPENDIXA:
DataInputGuide71
LISTOFFIGURES
FigurePage
2.1ProgramStructureofLEWASTE7
4.1Problemdefinitionandsketchforexample1...................33
4.2FiniteelementdiscretizationforExample1...................33
4.3Conncentrationprofilesatvarioustimes....................34
4.4Problemdefinitionandsketchforexample2...................44
4.5FiniteelementdiscretizationforExample2...................44
4.650%Conncentrationcontoursatvarioustimes..................45
4.7Problemdefinitionandsketchforexample3...................56
4.8FiniteelementdiscretizationforExample3...................57
4.9ThevelocityfieldfromFEMWATERsimulation................58
4.1050%Conncentrationcontoursatvarioustimes..................59
LISTOFTABLES
TablePage
4.1InputDataSetforExample135
4.2PartialListingofOutputforExample137
4.3InputDataSetforExample247
4.4PartialListingofOutputforExample249
4.5InputDataSetforExample362
4.6PartialListingofOutputforExample364
ABSTRACT
Thisdocumentpresentstheusers'manualofLEWASTE,aHybridLagrangian-EulerianFiniteElementModelofWASTETransportthroughSaturated-UnsaturatedMedia.Incomparisontoconventionalfiniteelement(includingbothGalerkinandupstreamfiniteelements)orfinitedifference(includingbothcentralandupwindfinitedifferences)models,LEWASTEoffersseveraladvantages:
(1)itcompletelyeliminatesnumericaloscillationduetoadvectionterms,
(2)itcanbeappliedtomeshPecletnumberrangingfrom0toinfinity(conventionalfiniteelementorfinitedifferencemodelstypicallyimposeundulysevererestrictiononthemeshPecletnumber),(3)itcanuseverylargetimestepsizetogreatlyreducenumericaldispersion(infact,thelargerthetimestep,thebetterthesolutionwithrespecttoadvectiontransport;thesizeoftimestepsizeisonlylimitedbytheaccuracyrequirementwithrespecttodiffusion/dispersiontransport,whichisnormallynotaverysevererestriction),and(4)thehybridLagrangian-Eulerianfiniteelementapproachisalwayssuperiortoandneverbeworsethanitscorrespondingupstreamfiniteelementmethod).Becauseoftheseadvantages,LEWASTEisintendedtosupersedeitspredecessorFEMWASTE(AFiniteElementModelofWASTETransportthroughSaturated-UnsaturatedPorousMedia).Themodelisdesignedforgenericapplications.Foreachsite-specificapplication,36maximumcontrol-integersmustbeassignedintheMAIN.Inputtotheprogramincludesthecontrolindices,propertiesofthemedia,thegeometryintheformofelementsandnodes,andboundaryandinitialconditions.Principaloutputincludesthespatialdistributionofconcentrationsandmaterialfluxcomponentsatanydesiredtime.Fluxesthroughvarioustypesofboundariesareoutput.Inaddition,diagnosticvariables,suchasthenumberofnon-convergentnodesandresidualsmaybeprintedifrequired.
1.INTRODUCTION
LEWASTE(AHybridLagrangian-EulerianFiniteElementModelofWASTESTransportthroughSaturated-UnsaturatedMedia)isintendedtosupersedeFEMWASTE(AFiniteElementModelofWASTETransportthroughSaturated-UnsaturatedPorousMedia),butalsoincludesFEMWASTEasanoption.UsingthehybridLagrangian-Eulerianapproach,onecancompletelyeliminatenumericaloscillationduetoadvectiontransport.Largetimestepsizescanbeusedtoovercomeexcessivenumericaldispersion.Theonlylimitationonthesizeoftimestepistherequirementofaccuracywithrespecttodispersiontransport,whichdoesnotposemuchsevererestrictions.
Thepurposeofthismanualistoprovideguidancetousersofthecomputercodetoenablethemtoemploythemodelforsite-specificapplication.Thus,Section2.1liststhegoverningequationsandinitialandboundaryconditionsforwhichLEWASTEisdesignedtosolve.Section2.2containsthedescriptionofallsubroutinesinLEWASTE.Thisshouldfacilitatetheunderstandingofthecodestructurebytheusers.Sinceoccasionsmyarisethattheusershavetomodifythecode,thissectionshouldhelpthemtotracethecodesotheycanmakenecessaryadjustmentsfortheirpurposes.Section3.1containsthespecificationofmaximumcontrol-integers.Foreachapplication,theuserneedstoassign32maximumcontrol-integersintheMAIN.Section3.2describesfilesrequiredfortheexecutionofLEWASTE.AppendixAcontainsthedatainputguidethatisessentialforanysitespecificapplication.Theusersmaychoosewhateverunitshewantstouseprovidedtheyaremaintainedinalltheinput.Unitsofmass(M),length(L),andtime(T)areindicatedintheinputdescription.
ThespecialfeaturesofLEWASTEareitsflexibilityandversatilityinmodelingaswidearangeofproblemsaspossible.Themodelisdesignedto:
(1)treatheterogeneousandanisotropicmediaconsistingasmanygeologicformationasdesired,
(2)considerspatiallyandtemporallydistributedaswellaspointsources/sinks,(3)accepttheprescribedinitialconditionsortoobtainthembysimulatingsteadystateversionofthesystemunderconsideration,(4)dealwithprescribedtransientconcentrationdistributedovertheDirichletboundary,(5)handletimedependentfluxesovervariableboundaries,(6)dealwithtimedependenttotalfluxesoverCauchyboundaries,(7)includetheoff-diagonaldispersioncoefficienttensorcomponentsingoverningequationfordealingwithcaseswhenthecoordinatesystemdoesnotcoincidewiththeprincipaldirectionsofthedispersioncoefficienttensor,(8)providetwooptionsoftreatingthemassmatrix-consistentandlumping,(9)givethreeoptions(exactrelaxation,under-andover-relaxation)forestimatingthenonlinearmatrix,(10)includesixoptionsforsolvingthelinearizedmatrixequations:
directGaussianelimination,successivepointiterationsolutionstrategies,polynomialpreconditionedconjugategradientmethod,incompleteCholeskypreconditionedconjugategradientmethod,modifiedincompleteCholeskypreconditionedconjugategradientmethod,andsymmetricsuccessiveover-relaxationpreconditionedconjugategradientmethod,(11)includebothquadrilateralandtriangularelementstofacilitatethediscretizationoftheregion,(12)automaticallyresettimestepsizewhenboundaryconditionsorsource/sinkschangeabruptly,(13)checkthemassbalancecomputationover
theentireregionforeverytimestep,(14)includethreeadsorptionmodels-thelinearisothermandthenonlinearFreundlichandLangmuirisotherms,and(15)includethehybridLagrangian-EulerianandtheconventionalEulerianapproaches.
2.THELEWASTEPROGRAMSTRUCTURE
2.1ThePurposeofLEWASTE
LEWASTEisdesignedtosolvethefollowingsystemofgoverningequationsalongwithinitialandboundaryconditions,whichdescribethematerialtransportthroughgroundwatersystems.Theequationsarederivedbasedonthecontinuityofmassandfluxlaws.Themajorprocessesareadvection,dispersion/diffusion,adsorption,decay,thecompressibilityofmedia,biodegradationthroughbothliquidandsolidphases,andsource/sink.
GoverningEquations-
(2.1)
(2.2a)
(2.2b)
(2.2c)
whereisthemoistureconcentration,bisthebulkdensityofthemedium(M/L3),Cisthematerialconcentrationinaqueousphase(M/L3),Sisthematerialconcentrationinadsorbedphase(M/M),tistime,Visthedischarge,isthedeloperator,Disthedispersioncoefficienttensor,isthedecayconstant,Fisastoragecoefficientrepresentingtheeffectofwatercapacityandcompressibilityofwaterandmedia(thedefinitionofFcanbefoundinFEMWATER),'isthecompressibilityofthemedia,histhepressurehead,Kwisthebiodegradationrateconstantthroughaqueousphase,Ksisthebiodegradationrateconstantthroughadsorbedphase,Qisthesourcerateofwater,Cinisthematerialconcentrationinthesource,Kdisthedistributioncoefficient,SmaxisthemaximumconcentrationallowedinthemediumintheLangmuirnonlinearisotherm,nisthepowerindexintheFreundlichnonlinearisotherm,andKisthecoefficientintheLangmuirorFreundlichnonlinearisotherm.
ThedispersioncoefficienttensorDinEq.(2.1)isgivenby
(2.3)
where│V│isthemagnitudeofV,istheKroneckerdeltatensor,aTisthelate
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