土壤溶质运移数学模型研究

西安理工大学博士学位论文土壤溶质运移数学模型研究姓名：张德生申请学位级别：博士专业：水文学及水资源指导教师：沈晋;沈冰20040101I::::::200411.2.-LaplaceMathematica-II3.BesselBesselLaplaceMathematicaMatlab4.LaplaceMathematica5.-LaplaceBesselMatlabMathematica(59879022)AbstractIIISTUDYONTHEMATHEMATICALMODELOFSOLUTETRANSPORTTHROUGHSOILSSubject:WaterResourcesandHydrologyAuthor:ZhangDeshengSignature:Tutor:ShenJinProfessorSignature:ShenBingProfessorSignature:Date:Jan.,2004AbstractConnectedwiththeprojectMechanismsforsolutetransportthroughsoilsandfittingmodelsintheloessareasupportedbytheNationalNaturalScienceFoundationofChina,themathematicalmodelsofwaterflowandsolutetransportthroughsoilsaretheoreticallystudiedandthemodelsofsolutetransportthroughsoilswhichcanbothreflectthemechanismsforsolutetransportthroughsoilsandbefitforthedemandofpracticalworkarepresented.Whilethesolutionsforthemodelsarecalculatedandsomevaluableresultsareobtainedasfollows:1.Thenumericalmodelofone-dimensionalverticalwaterinfiltrationthroughunsaturatedsoilsisconstructedbythecharacteristicfiniteelementmethod.Byusingtheanalyticalsolutionforaspecialcase,themathematicalverificationforthenumericalmodelisperformedandthevalidationofthenumericalmodelisensured.ThenumericalsimulationfortheinfiltrationtestofXi’anloessisdonebythecharacteristicfiniteelementnumericalmodelandthemodelingeffectisexact.2.Theadvection-dispersionmodelofone-dimensionalreactionsolutetransportthroughsoilswithdepth-dependentfirst-orderdegradationanddepth-dependentlinearequilibriumsorptionundersteadystateflowispresented.Thequasi-analyti-calexpressionsoftherelativeconcentrationsarededucedrespectivelybyusinghypergeometricequation,hypergeometricfunctionandthemethodofLaplacetransformundertheinitialconcentrationzeroandthefirstorsecondboundaryconditionofasemi-infiniteone-dimensionalspace.ThealgorithmsfortherelativeIVconcentrationscalculatedbyMathematicasoftwarepackagearegivenandthecomputationsforfoursupposedtestcasesareperformedseparately.Itcanbeseenfromtheresultsofcomputationthatthesimulationresultofthemodelisfitforthelawofreactionsolutetransportthroughsoils.Themodelisdiscretizedbythecharacteristicfiniteelementmethodandthecorrespondingcharacteristicfiniteelementnumericalmodelisobtained.Asfarasthenumericalmodelisconcerned,thenumericalcomputationsforthefoursupposedtestcasesarealsoperformed.Itcanbeseenfromcomparingthenumericalsolutionstothequasi-analyticalsolutionsthattheerrorscausedbythenumericalcomputationtotheadvection-dis-persionmodelofone-dimensionalreactionsolutetransportthroughsoilsundersteadystateflowusingthecharacteristicfiniteelementnumericalmodelobtainedinthepaperaresosmallthatthenumericalmodelperfectlymeetsforthedemandofcalculatingprecisioninpracticalwork.3.Thedispersivityisgeneralizedasalinearfunctionofsolutetransportdistanceandthetwo-regionmodelofone-dimensionalsolutetransportthroughheterogeneoussoilsconsideringscale-dependentdispersionandimmobileregionundersteadystateflowispresented.Moreover,thequasi-analyticalexpressionsoftherelativeconcentrationsatthemobileregionandtheimmobileregionarededucedrespectivelybyusingBesselequation,BesselfunctionandthemethodofLaplacetransformundertheinitialconcentrationzeroandthefirstorsecondboundaryconditionofasemi-infiniteone-dimensionalspace.WhilealgorithmsfortherelativeconcentrationscalculatedbyMathematicasoftwarepackageorMatlabsoftwarepackagearegivenandthecomputationforthesupposedtestcaseareperformed.Itcanbeseenfromtheresultsofcomputationthatthesimulationresultofthemodelissuitableforthelawofsolutetransportthroughsoils.Themodelisdiscretizedbythecharacteristicfiniteelementmethodandthecorrespondingnumericalmodelisobtained.Inthetermsofthenumericalmodel,thenumericalcomputationforthesupposedtestcaseisalsoperformed.Itcanbeseenfromcomparingthenumericalsolutionstothequasi-analyticalsolutionsthattheerrorscausedbythenumericalcomputationtothetwo-regionmodelundersteadystateflowusingthecharacteristicfiniteelementnumericalmodelobtainedinthepaperareverysmallandthenumericalmodelcanmeetforthedemandofpracticalwork.4.Thedispersivityisgeneralizedasanexponentialfunctionofsolutetransportdistanceandthetwo-regionmodelofone-dimensionalsolutetransportthroughAbstractVheterogeneoussoilsconsideringscale-dependentdispersionandimmobileregionundersteadystateflowispresented.Thequasi-analyticalexpressionsoftherelativeconcentrationsatthemobileregionandtheimmobileregionarededucedrespectivelybyusinghypergeometricequation,hypergeometricfunctionandthemethodofLaplacetransformundertheinitialconcentrationzeroandthefirstorsecondboundaryconditionofasemi-infiniteone-dimensionalspace.WhilethealgorithmsfortherelativeconcentrationscalculatedbyMathematicasoftwarepackagearegivenandthecomputationforthesupposedtestcaseareperformed.Itisknownfromthecalculatingresultsthatthesimulationresultofthemodelisconsistencewiththelawofsolutetransportthroughsoils.Moreover,themodelisdiscretizedbythecharacteristicfiniteelementmethodandthecorrespondingnumericalmodelisobtained.Thenumericalcomputationforthesupposedtestcaseusingthenumericalmodelisalsoperformed.Aconclusioncanbedrawnf