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How to? Extra term in k-e equation. Implicit-Explicit

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Old   March 15, 2013, 08:48
Default How to? Extra term in k-e equation. Implicit-Explicit
  #1
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M. Montero
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Hi all,

I am trying to implement a canopy model into OF.
With respect to the momentum equation, I am seeing several post where the code was similar to the following one:
Quote:
// Solve the Momentum equation
UEqn() == -fvc::grad(p)-fvm::Sp(mag(fvc::Sp(Cd*canopydensity*canopyleaf,U) ),U)
The point is when I need to implement the extra terms in k and epsilon equation.
I have introduced the following ones:
Quote:
// Turbulent kinetic energy equation

volScalarField Fk=0.8*canopydensity_*canopyleaf_*mag(U_)*mag(U_)* mag(U_);
tmp<fvScalarMatrix> kEqn
(
fvm::ddt(k_)
+ fvm::div(phi_, k_)
+ fvm::SuSp(-fvc::div(phi_), k_)
- fvm::laplacian(DkEff(), k_)
==
G
- fvm::Sp(epsilon_/k_, k_) + Fk

// Dissipation equation
volScalarField Fe=(epsilon_/k_)*Cpepsilon1_*Fk;
tmp<fvScalarMatrix> epsEqn
(
fvm::ddt(epsilon_)
+ fvm::div(phi_, epsilon_)
+ fvm::SuSp(-fvc::div(phi_), epsilon_)
- fvm::laplacian(DepsilonEff(), epsilon_)
==
C1_*G*epsilon_/k_
- fvm::Sp(C2_*epsilon_/k_, epsilon_) + Fe
It compiles correctly and I obtain some physical results, but I have just found a master thesis where:

Quote:
// Dissipation equation
tmp<fvScalarMatrix> epsEqn
(
fvm::ddt(epsilon_)
+ fvm::div(phi_, epsilon_)
- fvm::Sp(fvc::div(phi_), epsilon_)
- fvm::laplacian(DepsilonEff(), epsilon_)
==
C1_*G*epsilon_/k_
- fvm::Sp(C2_*epsilon_/k_, epsilon_)
+ fvm::Sp(Cd_*alphaL_/k_*(CEps4_*betap_*pow(mag(U_),3)-CEps5_*betad_*k_*mag(U_)), epsilon_); //Source Term)
// Turbulent kinetic energy equation
tmp<fvScalarMatrix> kEqn
(
fvm::ddt(k_)
+ fvm::div(phi_, k_)
- fvm::Sp(fvc::div(phi_), k_)
- fvm::laplacian(DkEff(), k_)
==
G
- fvm::Sp(epsilon_/k_, k_)
+ fvm::Sp(Cd_*alphaL_/k_*(betap_*pow(mag(U_),3)-betad_*k_*mag(U_)), k_); //Source term)
The question are:

Is correct my implementation?

what is the advantages to take the extra terms as implicit in the k and epsilon equation with respect to take them as explicit terms? Quick Convergence? Stability?

Thank you very much for your time.
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Old   March 19, 2013, 11:50
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M. Montero
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Ok, It seems according to the other topic that it is related to the stability of the equations...
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