Anewmethodforsloshingsimulationinaswaytankispresent,inwhichthetwophaseinterfaceistreatedasaphysicaldiscontinuity,whichcanbecapturedbyawell-designedhighorderscheme.BasedonNormalizedVariableDiagram(NVD),ahighorderdiscretizationschemewithunstructuredgridsisrealized,togetherwithanumericalmethodforfreesurfaceflowwithafixedgrid.Thismethodisimplementedinanin-housecodeGeneralTransportEquationAnalyzer(GTEA)whichisanunstructuredgridsfinitevolumesolver.Thepresentmethodisfirstvalidatedbyavailableanalyticalsolutions.Asimulationfora2-Drectangulartankatdifferentexcitationfrequenciesoftheswayiscarriedout.AcomparisonwithexperimentaldatainliteratureandresultsobtainedbycommercialsoftwareCFXshowsthatthesloshingloadonthemonitorpointsagreeswellwiththeexperimentaldata,withthesamegrids,andthepresentmethodgivesbetterresultsonthesecondarypeak.Itisshownthatthepresentmethodcansimulatethefreesurfaceoverturningandbreakupphenomena.