华中科技大学有限差分作业终稿

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1、华中科技大学研究生课程考试答题本考生姓名考生学号系、年级类别考试科目_考试日期题号得分题号得分总分：评卷人：注：1、无评卷人签名试卷无效。2、必须用钢笔或圆珠笔阅卷，使用红色。用铅笔阅卷无效。题号回答内容得分Pleasededucethesecond-orderforwarddifferential,second-orderbackwarddifferentialandsecond-ordercentraldifferentialofy=f（x）,thendeducetheprecisionofy=f（x）second-ordercentraldiffere

2、ntiaL（10points）Answer：（1）Firstofall,threedifferentialformulaaregivenasfollows:Thesecond-orderforwarddifferentialformula：二△（△『）二△［/（兀+心）_/（兀）］Ax2Ax2Ax2_纣（兀+Ax）-纣（兀）■ZP_Lf（兀+2Ar）—/（兀+Ax）］—［/（兀+心）一/（兀）］二/（x+2Ax）-2/（兀+心）+/⑴Ax2Thesecond-orderbackwarddifferentialformula：△［/（%）—/（兀一心）］Aa-

3、2Ax2Ar2二A/XQ--心）心2_［/（兀）一/（兀一心11一［/（兀一心）一/（兀一2心）［ZP_/（兀）一2/（兀一心）+/0-2心）Thesecond・ordercentraldifferentialformula：A2y_△（△『）_+Ax2Ax2Ax2A/（兀+一（x—*心）Ax2_［/（兀+心）—/（x）］_y（x）—/（x—M）］-2=才0+4兀）_2于（兀）+Ax2（2）Thefunctionf（x+Ar）andf{x-Ar）areexpandedatthepointofxtillthe3rdorderwiththeremainderom

4、itted,/(x4-Ax)—f(x)+f(x)Ax4-2〔(山)+3〕(心)+O((Ax))fixAr)-f(x)f(x)Ar+(Ax)(心)+O((Aa))J•J•ThenbringtheTaylorexpansionof/(x+Ax)and/(x-Ax)tothesecond・ordercentraldifferentialformula,afterrearrangingwegetthatA2y_/(x+Ax)-2/(x)+/(兀_Ax)Ax2Ax2=r(x)+O((Ax)2)Nowwecansaythattheprecisionofthesecond

5、-ordercentraldifferentialformulais2.题号回答内容得分Q2题号回答内容得分Q3PleasesimulatethetemperaturefieldofancastingusingFDM.Thegeometricconditionsandinitialconditionsareasfollows:1)ThematerialofthecastingisZG25,theenvironmenttemperatureis25°Candthemoldmaterialisresinsand;2)Pouringtemperatureis156

6、0°C;3)Choosingacastinggeometry,themoldthicknessis40mm.Requirements:1)Writeoutthe2Dor3Dmathematicalmodelthatdescribesthetemperaturefieldofthecastingcoolingprocess;(10points)2)DeducetheFDMformatofthemathematicalmodel;(10points)3)DrawtheFDMgridmap,anddescribeitusingdatastructure;(10po

7、ints)4)GivethethermalpropertiesparametersofZG25,resinsandandtheair;(10points)5)Programtosimulatethisphysicalprocess,assumingthecavitywasfilledveryfastandtheinitialtemperatureevenlydistributed.Pleaseprovidethemaincodeoftheprogram.(25points)6)Howlongdoesittakewhilethehighesttemperatu

8、reofthecastingdropsto1450°