HAL Id: inria-00088040
https://hal.inria.fr/inria-00088040v2
Submitted on 1 Aug 2006
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Strategies for RANS/VMS-LES coupling
Gennaro Pagano, Simone Camarri, Maria Vittoria Salvetti, Bruno Koobus, Alain Dervieux
To cite this version:
Gennaro Pagano, Simone Camarri, Maria Vittoria Salvetti, Bruno Koobus, Alain Dervieux. Strategies for RANS/VMS-LES coupling. [Research Report] RR-5954, INRIA. 2006, pp.43. �inria-00088040v2�
a p p o r t
d e r e c h e r c h e
ISRNINRIA/RR--5954--FR+ENG
Thème NUM
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Strategies for RANS/VMS-LES coupling
Gennaro Pagano, Simone Camarri, Maria Vittoria Salvetti, Bruno Koobus, Alain Dervieux
N° 5954
July 2006
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¥:e£wsx¶qyqye0t¾o+¯±~6´~£o
¿
∂W
∂t , χl
+ (∇ ·Fc(W), χl) + (∇ ·Fv(W), φl) = 0 l= 1, N » ¼
£`%e0wse
(·,·) pe0tc~qye<oqy`%e
L2 os0w cws~ncu%ÂqL·
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t%
VF E
·
wse<oy :e<Âqsx´µ6e0m®o OtctceL¥|m
χl
t%
φl
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¿
VF V =VF V
MVF V0 ; VF E =VF E
MVF E0 » ¼
xt#£`%x` Lpe<tc~qse<oqy`cepxwse<Âqou%d t%
VF V
tO
VF V0 wyeNqy`ce'%tcx´qye+µ~6´ucdKe+o %6eLo 6oyoy~px{qyeL
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χl
t%
χ0lÇ VF E
t%
VF E0 wseqy`ce '%tcx´qye²e0e0dKe0t|qt%´~6~uOo0¬T$ºt«e¯r¬NPVULCR8® cwy~re<qy~w~ :e0wqy~6w
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¿
W =P(W) =X
k
V ol(Ck) X
jIk
V ol(Cj) X
jIk
χj
| {z }
χk
Wk »6¼
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¿
W =P(W) =X
k
V ol(Ck) X
jIk
V ol(Cj) X
jIk
φj
| {z }
φk
Wk
»QU<6¼
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Cj
x{o?qy`ce
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j· V ol(Cj)pe<tc~qse<o+x¶qo+µ~ucdKet%
Ik ={j/Cj∈Cm(k)}· Cm(k)
¥:e0xtc¸qy`cead0wy~³Á0e0|0~t|qsx´tcxtc?qy`ce0e0
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¿ χ0l=χl−χl t% φ0l=φl−φl¬
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¿
∂hWi+Wc
∂t , χl
+ (∇ ·Fc(hWi+Wc), χl) + (∇ ·Fv(hWi+Wc), φl) =− τLES(W0), φ0l
l= 1, N
»QUUL¼
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τLES
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µs
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¿
µs=ρ0Cs∆2q
Sij0 Sij0 »QUL¼
£`%e0wse
Cs
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Cs
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¿
∂hWi
∂t , χl
+ (∇ ·Fc(hWi), χl) + (∇ ·Fv(hWi), φl) =
− τRAN S(hWi), φl
l= 1, N
»QU<6¼
∂Wc
∂t , χl
+ (∇ ·Fc(hWi+Wc), χl)−(∇ ·Fc(hWi), χl) + (∇ ·Fv(Wc), φl) = (1−θ)
τRAN S(hWi), φl
− τLES(W0), φ0l
l= 1, N
»QU0|¼
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¢ oK O~|oyoyx¥c´e`c~6x0e¯±~6w
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¿
θ=F(ξ) =tanh(ξ2) »QU¼
£`%e0wse
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tOdKe0m
¿
+ ξ =µs
µt
·p£`cx{`¾xooy~Ku%oye<o¥ce0t%pxtc %wsdKeqye<wax´t°§f¸ke¯r¬TPVURÁ·
+ ξ = ∆
lRAN S
· lRAN S
¥:e0xtc®²qrmn cx{0Ae0t%qy`¾xtqy`ce ¢ f?k % cwy~|`©·nx[¬e6¬
lRAN S=k3/2
+ ξ = tLES
tRAN S
·
tLES
t%
tRAN S
¥:e0xtc«`%ws6Âqse0wsxoqyx{²qyxdeLo~¯+qs`ce§¨ªk½tO½ ¢ f¸k½ p³
cws~6`%e<o+wyeLo :e<qyxµe<´m6·
tLES= 1 qSij0 Sij0
t%
tRAN S=k
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¿
∂W
∂t , χl
+ (∇ ·Fc(W), χl) + (∇ ·Fv(W), φl) =
−θ τRAN S(hWi), φl
−(1−θ) τLES(W0), φ0l
l= 1, N
»QU<6¼
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¿
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¿
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· e ¥:e0xtcqy`cext|qye0wst%Ae0tce<wy6mp¼¬
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∂eui
∂xj
+∂uej
∂xi
−2 3
∂eul
∂xl
δij
| {z }
Peij
−2
3ρkδij , »QU ¼
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δij
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Lij¿
Lij =αRij=αµtPeij−2
3ρ(αk)δij , »QU ¼
£`%e0wse
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0≤α≤1¼Â·cµwymnxtc²xt°o Oet%®qsx´dKe6¬
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¿
α= min µs
µt
,1
»QU 6¼
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µs
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