简介：Inthispaper,ahigh-orderfinite-volumeschemeispresentedfortheone-dimensionalscalarandinviscidEulerconservationlaws.TheSimpson’squadratureruleisusedtoachievehigh-orderaccuracyintime.TogetthepointvalueoftheSimpson’squadrature,thecharacteristictheoryisusedtoobtainthepositionsofthegridpointsateachsub-timestagealongthecharacteristiccurves,andthethird-orderandfifth-ordercentralweightedessentiallynon-oscillatory(CWENO)reconstructionisadoptedtoestimatethecellpointvalues.Severalstandardone-dimensionalexamplesareusedtoverifythehigh-orderaccuracy,convergenceandcapabilityofcapturingshock.
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