城市暴雨内涝数学模型的研究与应用

1,2,1,3,4,1,3,4(11,300074;21,300072;31,210008;41,330046):,,,,,(),,,,:;;;;;:P33312:A:100126791(2005)0320384207:2004202220;:2004205230:(1955-),,,,E2mail:tjxyy2002@yahoo1com1cn,,,,[1],,,,,,,200331,[2],,,,,,,,,[3],,H,Q,,,,,,,,,16320055ADVANCESINWATERSCIENCEVol116,No13May,2005;,22816786462HT+2dti=HTi+2dtAi6Kk=1QikLik+2qT+dtidt(1)Aii;Likik,;Qikik;Hii;qii;dtTQik,,,,,()(),,[4,5]:QT+dtik=QT-dtik-2gHiZTik2-ZTik1dLikdt-2gn2ikQT-dtik|QT-dtik|H7/3idt(2)Zik1Zik2ik12;dLikik;nikik;g:QT+dtik=sign(ZTik1-ZTik2)H5/3i|ZTik1-ZTik2|dLik1/21nik(3),[6],QT+dtik=mikik2gH3/2i(4)mikik;ikik,,(4);Qs(2);:HT+2dtdi=HTdi+2dtAdi6Nk=1QT+dtikLik+62Nj=1QT+dtdijLdij/2+2qT+dtdidt(5)Adti;qdii,,;Hdii;Qdiji;Ldiji3,,,,[7],,,5833:,:,,;,,,:QT+dtpi=QT-dtpi-2gApiZTi2-ZTi1dLidt-2gn2QT-dtpi|QT-dtpi|ApiR4/3pidt(6)Qpi();dLi;Rpi;,Api;Zi1Zi2;,Api;Zi1,Zi2():HT+2dtpi=HTpi+2dtApi6Nk=1QT+dtpk+2qT+dt1AApidt(7)Hpi;q1;N;Api1Fig11Schemeofbumpingstation,damandweirindrainagesystem,,,,2222,1,,,,,;,4,,,N(x,y),n(nN),nq1,q2,,qn,,(x,y)q(x,y)=a1x2+a2y2+a3xy+a4x+a5y+a6(8)nR=6ni=1(q-qi)2(9),nR,683162Fig12SchemeofmeshesspecialpassageandloggingsiteinthemodelinTianjin5R5ai=0i=1,2,,n(10)(10)ai(i=1,2,,n),(8),(x,y)q5[8],,,,,,,,,323167km2,2199581617,,1,1998422(2),1Table1Correctresultofmaximalwaterdepth/m/m/m/%/m/m/m/%01400136-0104-01101700167-010301001600152-0108-01101600162010201001900184-0106-01101300129-010101001700160-0110-01101200120010001001100110010001001400137-0103-01101250128010301101500146-0104-01101150115010001001200120010001001300129-010101001300129-010101001400141010101001250125010001001400138-0102-01101150115010001001300129-010101001400136-0104-01101400136-0104-01101300129-010101001500145-0105-01101400138-0102-01101550156010101001300129-010101001300129-0101010()01450141-0104-01101350133-0102-01101350131-0104-01101300129-010101001350133-010201001400137-0103-0117833:2Table2Testingresultofmaximalwaterdepth/m/m/m/%/m/m/m/%01450150010501101600178011801301400133-0107-01201500149-010101001300126-0104-01101700184011401201400146010601101600178011801301900182-0108-01101550161010601101700164-0106-011015001510101010014001460106012014001520112013,1999830,,2002722,2002424,2003412,()6,,20033,3,(1)2003110110122003101012,48h,16016mm,100,1m,,,,,,,,,(110m),2281,177,2104,,3(2)2003171452003745,,420520,20712mm,,,01501120m,,,:710m;510m;678,106,,572,43Table3AbsoluteerrordistributionoftheactualandthesimulatedwaterdepthinTianjin011m011012m012013m013m1947945589215%415%216%014%4Table4AbsoluteerrordistributionoftheactualandthesimulatedwaterdepthinNanjing011m011012m012013m013m331144306158%26%5%11%883164,20cm,84%11%30cm,30cm,92%(3)20031612324200362324150mm,,36,,,100m,,,,,,76m3/s3012m3/s:10m,5Table5AbsoluteerrordistributionoftheactualandthesimulatedwaterdepthinNanchang011m011012m012013m013m2861668%15%2%13%646,41,,,41(5)5,20cm,83%5%30cm30cm6,,347368,420120cm,7(1)1,11,,(2),,,(3),,,(4),22370cm,,345,,,,8(1),,,,(2):,,,9833::[1],,,.[J].,2000(11):34-421[2].[M].:,198914-1231[3].[M].:,1998.62-791[4],.[M].:,19881138-1571[5].[M].:,1990115-1201[6].()[M].:,1980.45-1091[7]HsuMH,ChenSH,ChangYJ.Inundationsimulationforurbandrainagebasinwithstormsewersystem[J].JournalofHydrology,2000,234(2):21-371[8]LiDa2ming,ZhangHong2ping,LiBing2fei,etal.Basictheoryandmathmaticalmodelingofurbanrainstormwaterlogging[J].JournalofHy2dramechanics,Ser1B,2004,16(1):17-271ResearchandapplicationofthemathematicalmodelforurbanrainstormwaterloggingXIEYi2yang1,LIDa2ming2,LIPei2yan1,SHENShu2qin3,YINJian2min4,HANSu2qin1,ZENGMing2jian3,GUXiao2qing4(11InstituteofTianjinMeteorologicalBureau,Tianjin300074,China;21SchoolofCivilEngineering,TianjinUniversity,Tianjin300072,China;31ObservatoryofJiangsuMeteorologicalBureau,Nanjing210008,China;41InstituteofJiangxiMeteorologicalBureau,Nanchang330046,China)Abstract:Inthispaper,amathematicalmodelforurbanrainstormwaterloggingisestablished,theroundflowandriverflowinthecityarethemainobjectstobesimulated1Themodelisestablishedonthebasisoftwo2dimensionalunsteadyflowtheoryandthetechniqueofnonstructuralandirregularmeshes1Amethodonthebasisofone2dimensionalunsteadyflowtheoryispro2posedtodealwithsmallscaleriver1Thedifferentdiscreteformsofmomentumequationsarederivedfordifferenttypesofpas2sageswhicharedividedintotherivertype,thegroundtypeandthespecialpassagetype(smallriverinthecities),Andthedischargeperunitwidthineachpassageofanygridiscomputedbythedifferentdiscreteformsofmomentumequations1Theflowinthedrainagepipenetworkissimulatedbyone2dimensionalunsteadyflowtheory,andthecalculationofthepumpingstations,thewatergatesandsubmersedpipesisindicated1Accordingtotheideaofthenonstructuralandirregularmeshes,thetopographiesareconsideredandthecalculationdomainsthatinvolveanypolygonaredesignedrespectivelyinTianjinCity,NanjingCityandNanchangCity1TheapplicationanderroranalysisofthemathematicalmodelinTianjin,NanjingandNan2changareshowed,too1Keywords:urbanrainstorm;floodofwaterlogging;mathematicalmodel;Tianjin;Nanjing;Nanchang,09316