hreeparts.
thefirstpart:threenumericalschemewerecheckedbycomparingtheirresultsfortheevolutionofsmallamplitudet-swaveswithresultobtainedbylinearstabilitytheory.
becauseitisverydifficulttocomparethecomputationalresultswiththoseobtainedbyexperiments,inordertocheckifthenumericalschemeusedwasaccurateenoughandiftheprogramwascorrect,threenumericalschemeshavebeenused,namely,thedscheme,a3rdorderanda5thorder,weaklyupwind,compactscheme.theatialevolutionofasmallamplitudet-swave,introducedattheinletofthemixinglayer,wascalculatedbyusingthesethreeschemes,andtheresultswerecomparedwiththoseobtainedbylinearstabilitytheory.theeffectonthemixingbyintroducingdisturbancewithfiniteamplitudeattheinlethasalsobeeninvestigatedbyusingthesethreedifferentschemes.theconclusionwas:forthefirstproblem,the5thordercompactschemesyieldresultcomparablewiththelinearstabilitytheory,whilethedschemewasnotsatisfactoryforthispurpose.whenthedisturbanceamplitudeexceeded0.01,duethenon-lineareffect,numericalresultsdeviatedfromthetheoreticalresults,implythatwhentheamplitudeofdisturbanceinasupersonicmixinglayerislargerthan0.01,itsevolutionwouldn
olongerfollowthelinearstabilitytheory.forthesecondproblem,thethreeschemesyieldedqualitativelythesameresult,andquantitatively,thedifferenceisnotbig.
thesecondpart
1.twonewmethodswereproposedtoverifytheexistenceofshockletsinducedbythedisturbanceina2-dsupersonicmixinglayer
theproblemofwhetherasimpleexteionofthenonlineartheoryofhydrodynamicstability,goodforincompre
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