Numerical_Grid_Generation

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1、PREFACENumericalgridgenerationhasnowbecomeafairlycommontoolforuseinthenumericalsolutionofpartialdifferentialequationsonarbitrarilyshapedregions.Thisisespeciallytrueincomputationalfluiddynamics,fromwhencehascomemuchoftheimpetusforthedevelopmentofthistechnique,buttheproceduresareequallyapplic

2、abletoallphysicalproblemsthatinvolvefieldsolutions.Numericallygeneratedgridshaveprovidedthekeytoremovingtheproblemofboundaryshapefromfinitedifferencemethods,andthesegridsalsocanservefortheconstructionoffiniteelementmeshes.Withsuchgridsallnumericalalgorithms,finitedifferenceorfiniteelement,a

3、reimplementedonasquaregridinarectangularcomputationalregionregardlessoftheshapeandconfigurationofthephysicalregion.(Finitevolumemethodsareeffectivelyatypeofconservativefinitedifferencemethodonthesegrids.)Inthistext,gridgenerationandtheusethereofinnumericalsolutionsofpartialequationsarebothd

4、iscussed.Theintentwastoprovidethenecessarybasicinformation,fromboththestandpointofmathematicalbackgroundandfromthatofcodingimplementation,fornumericalsolutionsofpartialdifferentialequationstobeconstructedongeneralregions.Sincethesenumericalsolutionsareultimatelyconstructedonasquaregridinare

5、ctangularcomputationalregion,anysolutionalgorithmthatcantreatequationswithvariablecoefficientsisbasicallyapplicable,andthereforediscussionofspecificalgorithmsislefttoclassicaltextsonthenumericalsolutionofpartialdifferentialequations.Theareaofnumericalgridgenerationisrelativelyyounginpractic

6、e,althoughitsrootsinmathematicsareold.Thissomewhateclecticareainvolvestheengineer’sfeelforphysicalbehavior,themathematician’sunderstandingoffunctionalbehavior,andalotofimagination,withperhapsalittlehelpfromUrania.Thephysicsoftheproblemathandmustultimatelydirectthegridpointstocongregatesotha

7、tafunctionalrelationshiponthesepointscanrepresentthephysicalsolutionwithsufficientaccuracy.Themathematicscontrolsthepointsbysensingthegradientsintheevolvingphysicalsolution,evaluatingtheaccuracyofthediscreterepresentationofthatsolution,communicatingthene