简介：APLU-SGSmethodbasedonatime-derivativepreconditioningalgorithmandLUSGSmethodisdevelopedinordertocalculatetheNavier-Stokesequationsatallspeeds.TheequationswerediscretizedusingAUSMPWschemeinconjunctionwiththethird-orderMUSCLschemewithVanLeerlimiter.ThepresentmethodwasappliedtosolvethemultidimensionalcompressibleNavier-Stokesequationsincurvilinearcoordinates.Characteristicboundaryconditionsbasedontheeigensystemofthepreconditionedequationswereemployed.Inordertoexaminetheperformanceofpresentmethod,driven-cavityflowatvariousReynoldsnumbersandviscousflowthroughaconvergent-divergentnozzleatsupersonicwereselectedtotestthismethod.Thecomputedresultswerecomparedwiththeexperimentaldataortheothernumericalresultsavailableinliteratureandgoodagreementsbetweenthemareobtained.Theresultsshowthatthepresentmethodisaccurate,self-adaptiveandstableforawiderangeofflowconditionsfromlowspeedtosupersonicflows.