一种基于移动最小二乘无网格法的自由面流动数值研究（英文）-豆柴文库

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一种基于移动最小二乘无网格法的自由面流动数值研究（英文）
AStudyofFree-SurfaceFlowNumericsBasedonMovingLeastSquaresUnstructuredGridMethod
Free-surfaceflowisatopicofgreatinterestinthefieldoffluidmechanics,asitisanaturalphenomenonthatoccursinmanyreal-lifesituations,includingoceanwaves,riverflows,andeventhesplashofastoneintoapond.Duetothecomplexnatureoffree-surfaceflows,accuratenumericalmethodsarenecessarytoproperlymodelthesephenomena.Inthispaper,weproposeanewapproachtomodelingfree-surfaceflowsbasedonthemovingleastsquaresunstructuredgridmethod.
Themovingleastsquares(MLS)methodisawell-establishedtechniqueforapproximatingscattereddata.Itinvolvestakingaweightedaverageofnearbydatapointstoobtainanestimateataspecificlocation.Inthecontextoffluidmechanics,thismethodhasbeenusedtointerpolatevelocityandpressurefieldsonunstructuredgrids.However,itsapplicationtofree-surfaceflowproblemshasbeenlimited,mainlyduetothedifficultyinaccuratelyrepresentingthefreesurface.
Toaddressthisissue,weproposeanovelapproachthatusestheMLSmethodtodirectlycomputethepositionofthefreesurface.Themethodinvolvesconsideringthefreesurfaceasasetofpointswithknownelevations,andusingtheMLSmethodtointerpolatethesurfaceelevationsatintermediatelocations.Inthisway,thefreesurfacecanberepresentedasacontinuousfunctionthatiseasytoworkwith.
Theunstructuredgridmethodisparticularlywell-suitedtomodelingfree-surfaceflows,asitallowsforgreaterflexibilityintheplacementofgridpoints.However,traditionalunstructuredgridmethodscanbecomputationallyexpensive,particularlyforlarge-scalesimulations.Toaddressthisissue,weproposeavariantofthemethodthatusesamovingleastsquaresinterpolationalongwithareducedbasisinordertocapturethecomplexdynamicsoffree-surfaceflowswitharelativelylownumberofdegreesoffreedom.
Tovalidateourmethod,weappliedittoanumberofbenchmarktestcases,includingthedam-breakproblemandthesloshingtankproblem.Ournumericalresultsdemonstratethatthemovingleastsquaresunstructuredgridmethodisabletoaccuratelycapturethecomplexdynamicsoffree-surfaceflowsinthesecases.Additi