(word完整版)一维地下水运动MATLAB模拟.doc

(word完整版)一维地下水运动MATLAB模拟
(word完整版)一维地下水运动MATLAB模拟
(word完整版)一维地下水运动MATLAB模拟
MACROBUTTONMTEditEquationSection2EquationChapter1Section1SEQMTEqn\r\h\*MERGEFORMATSEQMTSec\r1\h\*MERGEFORMATSEQMTChap\r1\h\＊MERGEFORMATError!Bookmarknotdefined.Problem1
Thegroundflowequationfor1Dheterogeneous,isotropicporousmediumwithaconstantaquiferthicknessisgivenby:

Whereh(x，t）isthehydraulichead，T(x）isthetransmissivity，andSisthestorativity.TheboundaryconditionsimposedareconstantheadhL（15m)andhR(5m)attheleftandrightendsofsoilcolumn，respectively.Theinitialconditionis0orrandomnumberateachnode.Thelengthofaquiferis1m（L=1m）.Thestorativityis1（S=1）。

DevelopaMATLABprogramwhichcanhandleaheterogeneoustransmissivityfieldusingtheimplicitmethod。
Testtheprogramforthecaseofhomogenousparameters,andcomparetheresultswiththeresultsgeneratedfromflowequationwithhomogenoustransmissivityfield(i.e.,)
Testtheprogramforpatch-heterogeneousTfield，whichcomprisesatwo—zoneTfieldwithafivefolddifferenceintransmissivity(T1=5T2,T1=0.01m2s—1，T2=0.002m2s-1;or,T1=0。2T2,T1=0。002m2s—1,T2=0。01m2s-1)andaninterfaceinthemiddleofthedomain。

Problem1解答
1理论推导
非均质一维地下水运动方程为： MACROBUTTONMTPlaceRef\＊MERGEFORMATSEQMTEqn\h\*MERGEFORMAT(SEQMTEqn\c\＊Arabic\*MERGEFORMATError!Bookmarknotdefined.)
如右图，各个点的水头分别为，水头和之间水力传导系数为.
将方程(1)进行离散化：设，则
MACROBUTTONMTPlaceRef\＊MERGEFORMATSEQMTEqn\h\＊MERGEFORMATError!Bookmarknotdefined.（SEQMTEqn\c\＊Arabic\*MERGEFORMATError!Bookmarknotdefined.)
MACROBUTTONMTPlaceRef\*MERGEFORMATSEQMTEqn\h\*MERGEFORMAT（SEQMTEqn\c\＊Arabic\*MERGEFORMATError!Bookmarknotdefined.)
MACROBUTTONMTPlaceRef\＊MERGEFORMATSEQMTEqn\h\*MERGEFORMAT(SEQMTEqn\c\*Arabic\*MERGEFORMAT3）
MACROBUTTONMTPlaceRef\*MERGEFORMATSEQMTEqn\h\＊MERGEFORMATError!Bookmarknotdefined.(SEQMTEqn\c\＊Arabic\＊MERGEFORMATError!Bookmarknotdefined.）
设则
MACROBUTTONMTPlaceRef\*MERGEFORMATSEQMTEqn\h\*MERGEFORMAT(SEQMTEqn\c\*Arabic\＊MERGEFORMATError!Bookmarknotdefined.）
MACROBUTTONMTPlaceRef\*MERGEFORMATS