基于结构网格下的AMR技术研究

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1、GlobalweaksolutionsofaninitialboundaryvalueproblemforscrewpinchesinplasmaphysicsSongJiangInstituteofAppliedPhysicsandComputationalMathematics,BeijingJointworkwithFengXie&JianwenZhang(箍缩)Sino-FrenchWorkshop,October20-24,NankaiUniv.,TianjinOutline：1.Governingequations2.Introductionofweak

2、solutions3.Globalexistence4.Ideaoftheproof1.GoverningEquationsMHDconcernsthemotionofaconductingfluid(plasma)inanelectromagneticfieldwithaverywiderangeofapplications.Thedynamicmotionsofthefluidandthemagneticfieldstronglyinteracteachother,andthusboththehydrodynamicandelectrodynamiceffects

3、havetobeconsidered.Thegeneralgoverningequationsof3DMHDread:Governingequations(Generalcase)Thesystemistoocomplextostudymathematically.Let’sconsideraspecialbutphysicallyveryinterestingcase:ScrewPincheswhichhaveveryimportantapplicationsinplasmaphysics.●ScrewpinchcaseConsiderancylindricalc

4、olumnofa(plasma)fluidwithanaxialcurrentdensityandaresultingazimuthalmagneticinduction.Thus,themagneticforce,actingontheplasma,forcestheplasmacolumntoconstrictradially.Thisradialconstrictionisknownasthepincheffect(firstbyBennett’34)magneticforce●ScrewpinchcaseScrewPinch:Magneticfieldline

5、swindaroundtheaxisinahelicalpathConsiderthecylindricalplasmafluidwithoutswirl,thenHence,inthescrewpinchcasethegeneralMHDequationsbecomesthefollowingsystemforRemarks:Screwpincheshaveimportantapplicationsinphysicsofplasmas,e.g.,“Tokamak”deviseswhichconfineandconstrict“hot”plasmatorealizen

6、uclearfusioninlabs.InsidetheTFTRVacuumVesselPrincetonPlasmaPhysicsLaboratoryTokamakFusionTestReactor(TFTR)JxB:directedtowardtothez-axis2)Z-pinchdeviseisanotherimportantpossibilitytorealizenuclearfusioninlabs.InitialphaseCompressionphasePinchexpansionphaseSandia’sZ-AccelaratorTime-exposu

7、rephotographofelectricalflashoverarcsproducedoverthesurfaceofthewaterintheacceleratortankasabyproductofZoperation.TheseflashoversaremuchlikestrokesoflightningMathematicaldifficulties:Singularityatx=0.Strongcoupling(interaction)ofthemagneticfieldandfluids3.Strongnonlinearities4.