简介:A3-DnumericalformulationisproposedonthehorizontalCartesian,verticalsigma-coordinategridformodelingnon-hydrostaticpressurefree-surfaceflows.Thepressuredecompositiontechniqueandθsemi-implicitmethodareused,withthesolutionprocedurebeingsplitintotwosteps.First,withtheimplicitpartsofnon-hydrostaticpressuresexcluded,theprovisionalvelocityfieldandfreesurfaceareobtainedbysolvinga2-DPoissonequation.Second,thetheoryofthedifferentialoperatorisemployedtoderivethe3-DPoissonequationfornon-hydrostaticpressures,whichissolvedtoobtainthenon-hydrostaticpressuresandtoupdatetheprovisionalvelocityfield.Whenthenon-orthogonalsigma-coordinatetransformationisintroduced,additionaltermscomeintobeing,resultingina15-diagonal,diagonallydominantbutunsymmetriclinearsysteminthe3-DPoissonequationfornon-hydrostaticpressures.TheBiconjugateGradientStabilized(BiCGstab)methodisusedtosolvetheresulting3-Dunsymmetriclinearsysteminsteadoftheconjugategradientmethod,whichcanonlybeusedforsymmetric,positive-definitelinearsystems.Threetestcasesareusedforvalidations.Thesuccessfulsimulationsofthesmall-amplitudewave,asupercriticalflowoverarampandaturbulentflowintheopenchannelindicatethatthenewmodelcansimulatewellnon-hydrostaticflows,supercriticalflowsandturbulentflows.
简介:Lid-drivenmixedconvectionhasbeengivenimmenseimportanceduetoitswiderangeofapplications.AT-shapedcavityisintroducedandpertinentparameterscontrollingmixedconvectionphenomenonareanalyzedinthispaper.Water-Al2O3nanofluidisconsideredinsidethecavitytoaugmentheattransferrate.Galerkinweightedresidualmethodoffiniteelementanalysisisappliedforthenumericalsimulations.Numericalsolutionisobtainedfordifferentsolidvolumefractionsofnanofluid(?=0-0.15),Grashofnumbers(Gr=0.1?5000)andReynoldsnumbers(Re=0.31?1000)inlaminarflowregime.Specialattentionisgivenontheanalysisofflowatthepuremixedconvectionregime.ItisfoundthatGrashof,ReynoldsandRichardsonnumbersalongwithsolidvolumefractionofnanofluidhavesignificanteffectonheattransfercharacteristicsinsidethecavity.ResultsarepresentedusingstreamlineandisothermcontoursalongwithrelatedvariationofaverageNusseltnumbersoftheheatedwallandaveragefluidtemperatureinsidethecavity.