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Publié par | chaeh |
Nombre de lectures | 25 |
Langue | English |
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THE FRENCH AEROSPACE LAB
w1EquationscostsandteNumericalCh?tillonAppClaudero,aHighc8th,hDGNumerical2exprmignone2rPimentsJSOSummayryOctoband0outlorenac@onera.frokreducedTimequelimplicit&hMaigh-o1rderONERA/DSNA/NUMFdiscontinuousCMAPGalerkinEcolemethoolydchniquewithreducedFidelitevaluationFlocostsSimulationsFloerrent201ReONERAnacflorent.1Implicit,withFevaluationrederic1/30CoTHE FRENCH AEROSPACE LAB
steadyecientEquationsDGandoNumericalschemeApp.roDGaofcrabhAntNumericalinexper-StokecedureruncouplingimentsinSummaDOFryofandexpoutlo,ok1997.Motivationcostsandracticalgoal3DDGeq.)metphrodd:locompactDOFstencilelement:owapplicationell-suitedoforrequationsunstructuredwithmeshes,etalgoErithmerpparenac@onera.frrallreducedelizations,pBCappapplication.(e.g.timeNaviexplicitesdiscretization:Aim:strongestimplicitCroFLforestrictiontheassomethoci:atedoftowparderrabsoliceachtermreconstructiontimehigherimplicitrderdiscretizatisoton:solutihighncompnonlineautatipaoolicnalnumericalcosterimentsiBR2nBassiducedal.b2ndyTC,thewlaen,rflorent.geImplicitnumbwitherevaluationof2/30DOFTHE FRENCH AEROSPACE LAB
ImplicitdiusionEquationscedureandSummaNumericalnApperimentsroraoutlocevaluationhpNumericalNumericalexpnonlineae2DrequationimentsanSummaflorent.rywithand3/30outloImplicitokroOutline21expEquations1DandrNumericalequationAppnonlinearoachdiusionNonlinea3rrydiusiondequationokEntroprenac@onera.fryDGsolutioreducedncostsSpacediscretizatioTHE FRENCH AEROSPACE LAB
2DSpaceEquationswithandNumericalNumericalanAppEntropropanonlineacequationhflorent.Numerical4/30expsolutioenrcedureimentserimentsSummadiusionryrandSummaoutlooutlookImplicitNonlineaevaluationrequationdiusionyequationnEntropdiscretizatioyImplicitsorolution2Spaceexpdiscretization1DImplicitrpequationrononlineacedurediusionOutline31ryEquationsdandokNumericalrenac@onera.frAppDGroachreducedNonlineacostsrdiusion−∇·( ( , )∇ ) = ( ) Ω⊂R
( , ) ∈R ∂Ω = Γ ∪Γ
= Γ
∇ · = Γ
−∇·( ( , )∇ ) = ( ) Ω×( ,∞)
( , ) = ( ) Ω
THE FRENCH AEROSPACE LAB
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U >
U
( , ) =U ( )
×∈R
( )
U =
( ) −∇·( ( )∇ ) = ( ) Ω×( ,∞)
THE FRENCH AEROSPACE LAB
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[
Ω = Ω
=
V ={ϕ∈ (Ω ): ϕ| ∈P (Ω ), = , }Ω
X
P (Ω )={ϕ∈ (Ω ): ϕ( , )= α φ ( , )}
=
∈V
X
( , )= φ ( ) ( ) ∀ ∈Ω , ∈( ,∞)
=
+ =
= ( + )( + )
=
THE FRENCH AEROSPACE LAB
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Z Z I Z
φ ( ) + ( θ )·∇φ − φ = φ ( )
Ω Ω ∂Ω Ω
θ , ∇ +
- +v vh hσ
= {∇ + }·
+Ω
-Ω
X
nσ
, ∀ ∈Ω
σ∈∂Ω
+ −Z Z +
{ }=σ + −
φ =− {φ}( − )
+ −Ω ∪Ω σ
THE FRENCH AEROSPACE LAB
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Z
= φ φ ( )
Ω
( + ) ( ) ( )
( − )+ ( ) =
( ) = ( Δ )
∂
= +
Δ ∂
= ×
O( )
THE FRENCH AEROSPACE LAB
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≤ ≤
< ≤
= =
+ +
+ +
v vh h
=
=
x xx xx j+ ½ x j+ ½j- ½ j- ½
+ - + -
THE FRENCH AEROSPACE LAB
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