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1、Compressiblehigh-speedgasflow6.1IntroductionProblemsposedbyhigh-speedgasflowareofobviouspracticalimportance.Applica-tionsrangefromtheexteriorflowsassociatedwithflighttointeriorflowstypicalofturbomachinery.Asthecostofphysicalexperimentsishigh,thepossibiliti
2、esofcomputationswereexploredearlyandthedevelopmentconcentratedontheuseoffinitedifferenceandassociatedfinitevolumemethods.Itwasonlyinthe1980sthatthepotentialofferedbythefiniteelementformswererealizedandthefieldisexpandingrapidly.Oneofthemainadvantagesintheu
3、seofthefiniteelementapproximationhereisitscapabilityoffittingcomplexformsandpermittinglocalrefinementwhererequired.However,theimprovedapproximationisalsoofsubstantialimportanceaspracticalproblemswillofteninvolvethree-dimensionaldiscretizationwiththenumbero
4、fdegreesoffreedommuchlargerthanthoseencounteredintypicalstructuralproblems(105-107DOFareherequitetypical).Forsuchlargeproblemsdirectsolutionmethodsareobviouslynotpracticableanditerativemethodsbasedgenerallyontransientcomputationformsareinvariablyused.Hereo
5、fcoursewefollowandacceptmuchthathasbeenestablishedbythefinitedifferenceapplicationsbutgenerallywilllosesomecomputationalefficiencyassociatedwithstructuredmeshestypicallyusedhere.However,thereductionoftheproblemsizewhich,asweshallsee,canbeobtainedbylocalref
6、inementandadaptivitywillmorethancompensateforthisloss(thoughofcoursestructuredmeshesareincludedinthefiniteelementforms).InChapters1and3wehaveintroducedthebasicequationsgoverningtheflowofcompressiblegasesaswellasofincompressiblefluids.Indeedinthelatter,asin
7、Chapter4,wecanintroducesmallamountsofcompressibilityintotheproceduresdevelopedtherespecificallyforincompressibleflow.Hereweshalldealwithhigh-speedflowswithMachnumbersgenerallyinexcessof0.5.Suchflowswillusuallyinvolvetheformationofshockswithcharacteristicdi
8、scontinuities.Forthisreasonweshallconcentrateontheuseoflow-orderelementsandofexplicitmethods,suchasthoseintroducedinChapters2and3.Herethepioneeringworkofthefirstauthor'scolleaguesMorgan,LohnerandPerairemustbe
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