Multiscale modelling of complex fluids: A mathematical initiation.
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Multiscale modelling of complex fluids: A mathematical initiation. C. Le Bris — T. Lelièvre. N° 6275 Août 2007. ISSN 0249-6399. apport de recherche. ISRN INRIA/RR--6275--FR+ENG. Thème NUM.
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(100) "$ =Q¨S ILN_ ªc´\cZT\dIuN $ # $ + " $ "%$³£mjfZdhlmFNGtk\dILN " " + ' $ "%$Û λ. . ∂τ p + u · ∇τ p − ∇uτ p − τ p (∇u)T ∂t. λ. ηp. . . . . η = 0. τ. η 6= 0. . ˙ + τ p = ηp γ,.
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(102) "$ A " . 2. MOh[t[uNGhF=b*Lc¦_"`L\dmO`Lb^_LNhFb^_[N ©³¦t[Ncb^MON_rNl _uNFZdrcho_uN\Rmjx`u¦ZRhobdbdMINGH bdc\dN(\^ILNlhFMOqLN \dNZsX[Zs\dNM hj@N;eo`rm\dchF_rZJ¦hFbR\dILN9¸Tft[b^hX[tY© ¹ ∂u + u · ∇u = (1 − )∆u − ∇p + div τ p , Re ∂t div u = 0, ∂τ p + u · ∇τ − (∇u)τ − τ (∇u)T = − 1 τ + ∇u + (∇u)T . p p p p ∂t We We + $ - Re > 0 We ∈ (0, 1) # > 0. Dz[Èz . u_HJHJhFIuIu_[NN ©³t[ cM9" NcfNGZ^_uZsZdNG$c_Bhox' _uNmjb^r0_B `u_YM#"`LMxxNb,NZ¤b hFÀ£\dILILcN-l,¤IZd\dXYILcfZsZON \dNG\dM IuNk" ÀZd'#b^N'%mjN"\dc·¤h #"eBhF`uRm\^\^cILhoNn_u!Z l,Iu" 2mjb,2 mF| l ¤\dNGxbdNcfZ]h\^cØl¦mFb^hFN_ubft mqLLb^mNG\^l ccfhoZd_¡NTt[\dcNMOu_LNkmjc\db^hjcNhF_u\d\dZILILNN MOZs\^mFcfl Lb^chocZs\]\dXb^`uhjl¢\^`L_Y`Lb^NGMOZ@Nc_b^clG\^mjIL§N*ZducM`uc`Ltmj\d\dhchF\^_uILZ NT=l,ZsIrNGmjNb,WYmFNGl\^l N\dcb^hFcZs_ \dcf2l \d2 cMO NThF§\dILNRu`Lcft ¤qLmÏX[Zml b^`ulcmFub^hFN*c_ \dILN ¡[ (' ! $. $ ! ! ' ! $ " " " $#! " + ! " # 1 ! # + ! $#' ! " $ ! " #! " $1 $ " ! $# # !" ' '%" "nNF u " ' # ! ' ' ' ! $# # % '#' "
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(124) N b^\c\s\d`uNGZR_"b^cN _\^`L\db^NG_"bdM\dhZhF\^IL
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(128)
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(131) ηp , Z(tr(τ p )) =
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