AnovelVOF-typevolume-trackingmethodfortwo-dimensionalfree-surfaceflowsbasedontheunstructuredtriangularmeshispresented.Owingtotheinherentmeritoftheunstructuredtriangularmeshinfittingcurvedboundaries,thismethodcanhandlethefree-surfaceproblemswithcomplexgeometriesaccuratelyanddirectly,withoutintroducinganycomplicatedboundarytreatmentorartificialdiffusion.ThemethodsolvesthevolumetransportequationgeometricallythroughtheModifiedLagrangian-EulerianRe-map(MLER)method,whichisappliedtoadvectivefluidvolumes.Moreover,thePLICmethodisadoptedtogiveasecond-orderreconstructedinterfaceapproximation.Tovalidatethismethod,twoadvectiontestswereperformedfortheestablishmentoftheaccuracyandconvergencerateofthesolutions.Numericalresultsforthesecomplextestsprovideconvincingevidencefortheexcellentsolutionqualityandfidelityofthemethod.
