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1、DevelopmentandstabilityanalysisoftheinverseLax-Wendroffboundarytreatmentforcentralcompactschemes1Fran¸coisVilar2andChi-WangShu3DivisionofAppliedMathematics,BrownUniversity,Providence,RI02912,USAAbstractInthispaper,wegeneralizetheso-calledinverseLax-Wendr
2、offboundarytreatment[23]fortheinflowboundaryofalinearhyperbolicproblemdiscretizedbytherecentlyintroducedcentralcompactschemes[14].Theoutflowboundaryistreatedbytheclassicalextrapolationandastabilityanalysisfortheresultingschemeisanalyzed.Toensurestabilityof
3、theconsideredschemesprovidedwiththechosenboundaries,theG-K-Stheory[9]isused,firstinthesemidiscretecasetheninthefullydiscretecaseusingthethird-orderTVDRunge-Kuttatimediscretization.Afterwards,duetothehighalgebracomplexityoftheG-K-Stheory,thestabilityisana
4、lyzedbyvisualizingtheeigenspectrumofthediscretizedoperators.Weshowthattheresultsobtainedwiththesetwodifferentapproachesareperfectlyconsistent.Wealsoillustratethehighaccuracyofthepresentedschemesonsimpletestproblems.KeyWords:Centralcompactschemes,initialb
5、oundaryvalueproblem,inverseLax-Wendroff,extrapolation,G-K-Stheory,eigenvaluespectrum.1ResearchsupportedbyNASAgrantNNX12AJ62A.2E-mail:francoisvilar@brown.edu3E-mail:shu@dam.brown.edu11IntroductionInnumericalsimulationofnumerousphysicalphenomena,thechoicei
6、ntheschemeusediscrucial.Forexampleinaeroacoustics,theflowsthatgeneratenoisesarenonlinear,unsteadyandusuallyturbulent.Thisaerodynamicnoiseisbroadbandwithafairlywidespectrum.Furthermore,theamplitudesofthephysicalvariablesoftheaerodynamicnoisearefarsmallert
7、hanthoseofthemeanflow,andthedistancefromthenoisesourcetothelocationofinterestinaeroacousticproblemsisquitelong.Regardingtheseremarks,toensurethatthecomputedsolutionisuniformlyaccurateoversuchalongpropagationdistance,thenumericalschemeshouldhaveminimalnum
8、ericaldispersionanddissipation,orinotherwordsshouldhaveagoodwaveresolutionandhighorderaccuracy.Arelevantchoiceistheclassofcompactschemes[3,12,15,18].Comparedtothespectralmethods,compactschemescanhandlenon-periodicboundaryconditio
