ASM及遗传算法 在地下水资源量评价中的应用.ppt

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1、Chapter2Equations&NumericalMethods1.1GoverningEquations1.1.1ConfinedAquiferThegoverningflowequationforconfinedaquifersisdevelopedfromapplicationofthelawofmassconservation(continuityprinciple)totheelementalvolume.Continuityisgivenby:Rateofmassaccumulation=Rateofmassinflow-RateofmassoutflowI

2、ntegratingtheconservationofmasswithDarcy’sLaw,thegeneralflowequationinthreedimensionsforaheterogeneousanisotropicmaterialisderived:Assumingthatthematerialishomogeneous,i.e.Kdoesnotvarywithposition,Equation2-19canbewrittenas:Ifthematerialisbothhomogeneousandisotropic,i.e.Kx=Ky=Kz,thenEquati

3、on2-21becomes:or,combiningpartialderivatives:Usingthedefinitionsforstoragecoefficient,(S=MSs),andtransmissivity,(T=KM),whereMistheaquiferthickness,Equation2-22becomes:Iftheflowissteady-state,thehydraulicheaddoesnotvarywithtimeandEquation2-22becomes:Equation2-24isknownastheLaplaceequation.1

4、.1.2UnconfinedAquiferInanunconfinedaquifer,thesaturatedthicknessoftheaquiferchangeswithtimeasthehydraulicheadchanges.Therefore,theabilityoftheaquifertotransmitwater(thetransmissivity)isnotconstant:Forahomogeneous,isotropicaquifer,thegeneralequationgoverningunconfinedflowisknownastheBousson

5、esqequationandisgivenby:Ifthechangeintheelevationofthewatertableissmallincomparisontothesaturatedthicknessoftheaquifer,thevariablethicknesshcanbereplacedwithanaveragethicknessbthatisassumedtobeconstantovertheaquifer.Equation2-26canthenbelinearizedtotheform:1.2MathematicModel1.2.1Unconfined

6、aquifer1.2MathematicModel1.2.2Confinedaquifer1.3NumericalMethods1.3.1FDM:FiniteDifferencesMethod1.3NumericalMethods1.3.2FEM:FiniteElementMethod