简介：Thispaperdescribestheuseofoverlappinggridsforthecalculationofflowaroundsingleandmultiple-particleconfigurationsatthemicroscale.ThebasicequationsforcalculationarethoseforconservationofmassandmomentumwhicharesolvedusingacommonFinite-Volumeformulation.Thehydrodynamicparticle-particleandparticle-wallinteractioncanbecalculatedbyusinganoverlappingorChimeragridscheme.Withthegridstructuringprocedureitispossibletousesimpleandstructuredgridsaroundtheparticlesandtheoverallmaingridgeometry.Theparticlegridsarelappedoverthemaingridsuchthattheycanmoveindependentlyaftereachtimestepwithoutremeshingthewholegeometry.Thepapergivesresultsforthevalidationofthecodedevelopedforgeneraltestcases,forarotatingellipsoidinsimpleshearflow,theflowaroundparticlesattachedtoawall,themotionofaparticleinthevicinityofawallandsomeresultsfortheflowthroughapackedbedconfiguration.

简介：Ithasbeenevidentthatthetheoryandmethodsofdynamicderivativesareplayinganincreasinglyimportantrleinhybridmodelingandcomputations.Beingconstructedonvariouskindsofhybridgrids,thatis,timescales,dynamicderivativesoffersuperioraccuracyandflexibilityinapproximatingmathematicallyimportantnat-uralprocesseswithhard-to-predictsingularities,suchastheepidemicgrowthwithun-predictablejumpsizesandoptionmarketchangeswithhighuncertainties,ascom-paredwithconventionalderivatives.Inthisarticle,weshallreviewthenovelnewconcepts,exploredelicaterelationsbetweenthemostfrequentlyusedsecond-orderdy-namicderivativesandconventionalderivatives.Weshallinvestigatenecessarycondi-tionsforguaranteeingtheconsistencybetweenthetwoderivatives.Wewillshowthatsuchaconsistencymayneverexistingeneral.Thisimpliesthatthedynamicderivativesprovideentirelydifferentnewtoolsforsensitivemodelingandapproximationsonhy-bridgrids.Rigorouserroranalysiswillbegivenviaasymptoticexpansionsforfurthermodelingandcomputationalapplications.Numericalexperimentswillalsobegiven.

简介：Aclassofnormal-likederivativesforfunctionswithlowregularitydefinedonLipschitzdomainsareintroducedandstudied.Itisshownthatthenewnormal-likederivatives,whicharecalledthegeneralizednormalderivatives,preservethemajorprop-ertiesoftheexistingstandardnormalderivatives.Thegeneralizednormalderivativesarethenappliedtoanalyzetheconvergenceofdomaindecompositionmethods(DDMs)withnonmatchinggridsanddiscontinuousGalerkin(DG)methodsforsecond-orderel-lipticproblems.Theapproximatesolutionsgeneratedbythesemethodsstillpossesstheoptimalenergy-normerrorestimates,eveniftheexactsolutionstotheunderlyingellipticproblemsadmitverylowregularities.

简介：这篇论文被奉献给非与动人的格子遵守有限元素计划的五个参数因为速度压力在2-D混合了非静止的Stokesproblem的明确的表达。我们证明这个元素有各向异性的行为并且基于一些新奇技术在速度和压力的一些某些标准导出各向异性的错误评价。特别通过我们得到的小心的分析，一致性错误评价上的有趣的结果，它从来没被看见过为混合了有限元素方法在以前文学。

简介：WeproposeanefficientandrobustalgorithmtosolvethesteadyEulerequa-tionsonunstructuredgrids.ThenewalgorithmisaNewton-iterationmethodinwhicheachiterationstepisalinearmultigridmethodusingblocklower-uppersymmetricGauss-Seidel(LU-SGS)iterationasitssmootherToregularizetheJacobianmatrixofNewton-iteration,weadoptedalocalresidualdependentregularizationasthereplace-mentofthestandardtime-steppingrelaxationtechniquebasedonthelocalCFLnumberTheproposedmethodcanbeextendedtohighorderapproximationsandthreespatialdimensionsinanatureway.Thesolverwastestedonasequenceofbenchmarkprob-lemsonbothquasi-uniformandlocaladaptivemeshes.Thenumericalresultsillustratedtheefficiencyandrobustnessofouralgorithm.

简介：Thispaperpresentsasimpleapproachforimprovingtheperformanceoftheweightedessentiallynonoscillatory(WENO)finitevolumeschemeonnon-uniformgrids.ThistechniquereliesonthereformulationofthefifthorderWENO-JS(WENOschemepresentedbyJiangandShuinJ.Comput.Phys.126:202–228,1995)schemedesignedonuniformgridsintermsofonecell-averagedvalueanditsleftand/orrightinterfacialvaluesofthedependentvariable.Theeffectofgridnon-uniformityistakenintoconsiderationbyaproperinterpolationoftheinterfacialvalues.Onnonuniformgrids,theproposedschemeismuchmoreaccuratethantheoriginalWENO-JSscheme,whichwasdesignedforuniformgrids.Whenthegridisuniform,theresultingschemereducestotheoriginalWENO-JSscheme.Inthemeantime,theproposedschemeiscomputationallymuchmoreefficientthanthefifth-orderWENOschemedesignedspecificallyforthenon-uniformgrids.Anumberofnumericaltestcasesaresimulatedtoverifytheperformanceofthepresentscheme.

简介：Themomentarystateofasemiconductordeviceisdescribedbyasystemofthreenonlinearpartialdifferentialequations.Afinitedifferenceschemeforsimulatingtransientbehaviorsofasemiconductordeviceongridswithlocalrefinementintimeandspaceisconstructedandstudied.Erroranalysisispresentedandisillustratedbynumericalexamples.

简介：LatticeBoltzmannmethodisoneofthewidelyusedinmultiphasefluidflow.However,thetwomaindisadvantagesofthismethodaretheinstabilityofnumericalcalculationsduetothelargedensityratiooftwophasesandimpossibilityofthetemperaturedistributiontobefedbackintothevelocitydistributionfunctionwhenthetemperatureissimulated.BasedonthecombinationprescribedbyInamuro,thelargedensityratiotwo-phaseflowmodelandthermalmodelmakesthedensityratioofthemodelsimulationtobeincreasedto2778:1byoptimizingtheinterfacedistributionfunctionoftwo-phasewhichimprovestheaccuracyofdifferentialformat.Thephasetransitiontermisaddedassourcetermintothedistributionfunctioncontrollingtwophaseorderparameterstodescribethetemperatureeffectonthegas-liquidphasetransition.Thelatentheatgeneratedfromthephasechangeisalsoaddedasasourcetermintothetemperaturedistributionfunctionwhichsimulatesthemovementoftheflowunderthecommoncouplingofdensity,velocity,pressureandtemperature.Thedensityandthetemperaturedistributionofsinglebubblearesimulated.Comparisonofthesimulationresultswithexperimentalresultsindicatesagoodagreementpointingouttheeffectivenessoftheimprovedmodel.

简介：AclassofnonlinearparabolicequationonapolygonaldomainΩR2isinves-tigatedinthispaper.Weintroduceafiniteelementmethodonoverlappingnon-matchinggridsforthenonlinearparabolicequationbasedonthepartitionofunitymethod.Wegivetheconstructionandconvergenceanalysisforthesemi-discreteandthefullydiscretefiniteelementmethods.Moreover,weprovethattheerrorofthediscretevariationalproblemhasgoodapproximationproperties.Ourresultsarevalidforanyspatialdimensions.Anumericalexampletoillustratethetheoreticalresultsisalsogiven.

简介：Thenonstaggeredgridsareadoptedinthispaperforsolvingthegoverningequationsofflowsinthecurvilinearcoordinatesystems.Thepresentpaperdemonstratesthebasicreasonandcorrespondingeliminatingmethodforthepressureoscillation,anddeducesthecorrectedexpressionsforthecurvilinearvelocitycomponentsinwhichandadditionaltermrepresentingthedifferencebetweenthe1-δand2-δdifferencevaluesforthepressuregradientappears.Thusifanoscillatorypressurefiledwerearisen,themagnitudeofthistermwouldbelargeandwouldacttoremovetheoscillation;whereasfornonoscillatoryfieldthemagnitudeofthistermremainssmall.Asexaminationforthenumericalmethod3-Dturbulentflowinasquareductwith90°bendand3-Dturbulentmixinglowinalobed-mixerwerecalculatiedrespectively.Thenumericalresultsaresatisfactory.

简介：这份报纸开发一个新方法在二和三种尺寸在矩形的格子上分析有限元素方法的重申的缺点修正计划的集中。主要想法是提出精力内部的产品和精力(半)标准进矩阵形式。然后，包含的二关键不平等的二个常数是min，二的最大特征值分别地联系概括特征值问题。这二个概括特征值问题的元素水平上的本地版本确切被解决突然地获得(更低)这二个常数的上面的界限。这和为重申的答案的一些必要观察在减少的2D和单调建立集中在3D的性质。为二种尺寸，结果此处在文学改进那些；为三种尺寸，结果此处是新的。数字结果被介绍检验理论结果。[从作者抽象]

简介：在这篇论文，我们在飞机为外面的传播问题涉及一个非重叠的领域分解方法(DDM)。基于自然边界积分操作员，我们把DDM与印射的Dirichlet-to-Neumann(DtN)相结合并且向数字分析提供非匹配格子。接口上的近似答案的弱连续性被一个双基础更多样地强加。我们显示出那这更多样地，空间能产生最佳的错误估计并且获得集中的相应的率。最后，几个数字例子证实理论结果。

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