Negative-concentrations(comsol中负浓度的处理方法)

ResultsWithSmallUnphysicalValuesWHEREANDWHYDOUNPHYSICALVALUESAPPEAR?Insomemodelssmallunphysicalvaluescanoccurduetonumericalartifacts.Examplesinclude:•Negativeconcentrationsinmasstransfer.•Atemperaturethatisslightlyhigherthantheinitialconditionintimedependentheattransferstudies.•Smallreactionforcesthatappearinunloadeddirectionsinstructuralmechanicsmodels.•Smallnegativegapsinacontactanalysis.•Smallnegativeeffectiveplasticstrainvalues.•Stressesabovetheyieldlimitforanideallyplasticmaterialinsolidmechanics.Somereasonsforwhytheseunphysicalvaluesoccur:•Numericalnoiseisacommoncause.Whenthevaluesofthedependentvariablesapproachzero,thenumericalnoisecanbecomerelativelysignificantandcausesomeoftheresultstobeslightlynegativeevenifthatisnotphysicallypossible.•Interpolationandextrapolationofvaluescancausesomevaluestobecomeunphysical.Forexample,resultsforanelastoplasticmaterialarecorrect(withinsometolerance)attheintegrationpoints(Gausspoints)insidethefiniteelements,butvaluesmightbecomeunphysicalwhenextrapolatingthedatatotheelementboundaries.•Discontinuitiesinthemodelisanothersourceof,forexample,smallnegativeconcentrationsduetoadiscontinuousinitialvalue.Withaninitialvaluethatiszeroalongaboundaryforaconvectivetransportmodels,forexample,thephysicalinterpretationisaninitiallysharp,graduallydiffusingfrontmovingawayfromtheboundary.However,forthedefaultshapefunction(second-orderLagrangeelements),onlycontinuousfunctionsareadmissibleassolutionsforthefiniteelementmodel.Theprogramthenmodifiesthediscontinuousinitialvaluebeforethetimesteppingcanbegin.Thisoftenresultsinasmalldipinthesolutionatthestarttime.Intheexamplemodelthatthefollowingfigureshows,theconcentrationislocallyslightlynegativeatt=0:•Lackofmeshresolutionisanothercauseofunphysicalvaluessuchasnegativeconcentrations.Theresultingconvergenceproblemsareoftentheunderlyingissuewhennegativeconcentrationsareobservedinhighconvectionregimes(highPecletnumber)andinthosewithlargereactiontermsorfastkinetics(highDamkohlernumber).•Incorrectphysicsinthemodelcanalsocausethesetypesofproblems.Formasstransfer,forexample,theuseofaconstantsinkinareactiontermisanapproximationthatonlyworksforlargeconcentrations.Whentheconcentrationreacheszero,thereactiontermcontinuestoconsumethespecies,finallyresultinginanegativeconcentration.AVOIDINGUNPHYSICALVALUESThissectioncontainssomewaystoavoidcomputingordisplayingunphysicalvalues:•Insomecasesitispossibletoaddabaselinetothedependentvariablesothatthenumericalnoisedoesnotaffectthesolutioninthesamewayaswhenthevaluesofthedependentvariableapproachzero.Thisscalingisnotpossiblewith,forexample,areactiontermthatdependsontheconcentrationbecausethenthescaleandorigindomatter.•Avoiddiscontinuitiesinthemodelbyusing,forexample,theavailablesmoothedstepfunctionsinstead.•Formulatelogarithmicvariablesasawayofeliminatingmeshresolutionproblemsandnegativedipsbyusingthelogarithmoftheoriginaldependentvariable(theconcentration,forexample)asthedependentvariable.Thereasonforthisisthatalinearlyvaryingmeshcansometimesnotcapturetheexponentialbehaviorofthechangesinthedependentvariable.Inaddition,modelingthelogarithmofthedependentvariableensuresthattherealconcentration,forexample,cannotbecomenegativeduringthesolutionprocess.•Avoiddisplayingsmallunphysicalvaluesduetonumericalnoisebyclippingthevaluesfortheplot.Youcandothisbyplotting,forexample,c*(c0)insteadofc,whichevaluatesto0everywherewherecissmallerthan0.Youcanalsoadjusttherangeoftheplotdataandcolorstoonlyshowvaluesthatarenonzero.Inthecasethatthedatarangechanges,partsoftheplotswherethevaluesareoutsidetherangebecomeempty.•Itcanalsobeusefultocheckhowthemeshaffectsthesolutionbyrefiningthemeshandcheckiftheproblemwithunphysicalvaluesgetsbetterorworse.Ifitgetsbetter,thencontinuetorefinethemesh.Ifitgetsworse,youprobablyneedtocheckthephysicsofthemodel.