LEWASTE Users Manual.docx

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