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divU-terms in k-eps equations

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Old   April 1, 2009, 10:43
Default divU-terms in k-eps equations
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Aram Amouzandeh
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Dear all!

Could somebody tell me please, where the terms

>> fvm::SuSp(((2.0/3.0)*C1_ + C3_)*rho_*divU, epsilon_)

and

>> fvm::SuSp((2.0/3.0)*rho_*divU, k_)

in the dissipation- and k-equation of the compressible RAS model come from (kEpsilon.C)? I searched the forum for further explanation but was not successful. Thanks in advance!!

Aram
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Old   June 18, 2009, 11:41
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Nat Trask
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They come from the double inner product of the velocity gradient with the Reynolds stress tensor in the production terms

i.e, for the epsilon equation, there should be a production term

C1*R_{ij}&&grad(U)

in the kEpsilon.C implemented in foam,
R_{ij} = (2.0/3.0)*I)*k_ - (mut_/rho_)*dev(twoSymm(fvc::grad(U_))

is split into two parts for stability reasons

the first term
C1_*G*epsilon_/k_
contains the contribution from the second term in the R_{ij} equation

the second term
- fvm::SuSp(((2.0/3.0)*C1_ + C3_)*rho_*divU, epsilon_)
contains the contribution from the (2/3)I*k term

Best,
Nat
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Old   June 19, 2009, 04:17
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Aram Amouzandeh
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Nat,

thanks a lot for the clarification!!

Best regards,
Aram
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