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1、AIAAJOURNALVol.36,No.11,November1998TechnicalNotesTECHNICALNOTESareshortmanuscriptsdescribingnewdevelopmentsorimportantresultsofapreliminarynature.TheseNotescannotexceed6manuscriptpagesand3gures;apageoftextmaybesubstitutedforagureandviceversa.Afterinformalreviewbytheeditors,theyma
2、ybepublishedwithinafewmonthsofthedateofreceipt.Stylerequirementsarethesameasforregularcontributions(seeinsidebackcover).OptimizedUpwindleavestwoofthecoefcients,e.g.,a¡Nanda¡NC1,asfreeparam-eters.TheseparametersarethenchosentominimizetheintegratedDispersion-Relation-Preservingerror
3、E.@E=@ajD0/,denedasFiniteDifferenceSchemefor¼=2¼=2EDj®N2®NComputationalAeroacousticsr1x¡®1xjd.®1x/C¸i1x00³´22M.Zhuang¤andR.F.Chen†®1x¡¼Csgn.c/exp¡2d.®1x/(3)MichiganStateUniversity,EastLansing,Michigan48824¾where¸and¾aretheadjustablepositiveconstants,®Nrand®Niaretherealandimaginary
4、partof®N,andcisthespeedofwaveprop-I.IntroductionagationinutCcuxD0,therst-orderlinearwaveequation.TheANYcompactandnoncompactoptimizedschemeswerere-optimizationprocesshastoallowthevaluesof®Nr1x¡®1xandMcentlyreviewedbyZingg.1Mostoptimizedschemes,how-®Ni1xtobeasclosetozeroaspossiblefo
5、rawiderangeofwaveever,arerestrictedtocentraldifferencealgorithms.Thisrestrictionnumbers.Theterm®Ni1xapproacheszeroinawayspeciedintheinevitablyleadstostabilityproblemsthatmustbedealtwiththroughsecondtermofEq.(3).Asimilarupwindschemewasstudiedbytheuseofltersorexplicitdissipationterm
6、s.AlthoughdeliberateLi5withadifferentapproachforoptimization.Unlikethecentralltersordissipationtermshaveprovedquitesuccessfulinmanyacousticproblems,2;3inthepresentstudytheoptimizedupwinddispersion-relation-preserving(DRP)nitedifferenceschemeisde-velopedtoimprovethequalityofthenume
7、ricalsolutionofshortwaveswithoutaddinganexplicitarticialdampingtermtothenitedifferenceequations.II.OptimizedUpwindDRPSchemeTheoptimizedupwindDRPschemedevelopedhereisbasedontheideaoftheDRPschemeproposedbyTamandWebb.4Considertheapproximationoftherstspatialderivative@u=@xbythenitedif
8、ferenceforauniformgridofspacing1x
