[MMRC]

Dear community, maybe my math skills are not current enough to confirm these 02 implementations are the same. Please check with me the production term and the FIRST term in the right side of the dissipation rate equation that for both software, are not the same, or are they?:


In openfoam ESI either 2012 or 2306 we have for production term:

const volScalarField::Internal divU
(fvc::div(fvc::absolute(this->phi(), U))().v() );
tmp<volTensorField> tgradU = fvc::grad(U);     const volScalarField::Internal GbyNu
     (
this->type() + ":GbyNu",
         tgradU().v() && dev(twoSymm(tgradU().v()))
     );
     const volScalarField::Internal G(this->GName(), nut()*GbyNu);
     tgradU.clear();

And, for epsilon equation this:

// Dissipation equation
      tmp<fvScalarMatrix> epsEqn
     (
         fvm::ddt(alpha, rho, epsilon_)
       + fvm::div(alphaRhoPhi, epsilon_)
       - fvm::laplacian(alpha*rho*DepsilonEff(), epsilon_)
      ==
         C1_*alpha()*rho()*GbyNu*Cmu_*k_()
 - fvm::SuSp(((2.0/3.0)*C1_ - C3_)*alpha()*rho()*divU, epsilon_)
 - fvm::Sp(C2_*alpha()*rho()*epsilon_()/k_(), epsilon_)
       + epsilonSource()
       + fvOptions(alpha, rho, epsilon_)
     );

In openfoam Foundation 9, we have for production term:

                           volScalarField::Internal divU
     (
         fvc::div(fvc::absolute(this->phi(), U))()
     );
 
 
     tmp<volTensorField> tgradU = fvc::grad(U);
     volScalarField::Internal G
     (
         this->GName(),
         nut()*(dev(twoSymm(tgradU().v())) && tgradU().v())
     );
     tgradU.clear();

And, for epsilon equation this:

  // Dissipation equation
                 tmp<fvScalarMatrix>             epsEqn
                 (
                     fvm::ddt(alpha,             rho, epsilon_)
                   +             fvm::div(alphaRhoPhi, epsilon_)
                   -             fvm::laplacian(alpha*rho*DepsilonEff(), epsilon_)
                  ==
                                 C1_*alpha()*rho()*G*epsilon_()/k_()
             -             fvm::SuSp(((2.0/3.0)*C1_ - C3_)*alpha()*rho()*divU, epsilon_)
              -             fvm::Sp(C2_*alpha()*rho()*epsilon_()/k_(), epsilon_)
                   +             epsilonSource()
                   +             fvModels.source(alpha, rho, epsilon_)
                 );

Key differences are:
1) In the section of Production G definition in ESI version, these variables are set as constants, would this imply they won't be modifiable while running the simulation?

2) Curiousity, is this math operation conmmutative of dot products commutative in order to asume that both source codes 'implements the same' ?

ESI:
const volScalarField::Internal GbyNu
(
IOobject::scopedName(this->type(), "GbyNu"),
tgradU().v() && devTwoSymm(tgradU().v())
);
const volScalarField::Internal G(this->GName(), nut()*GbyNu);


Foundation:
volScalarField::Internal G
(
this->GName(),
nut()*(dev(twoSymm(tgradU().v())) && tgradU().v())
);
3) The first term in RHS of dissipation equation... both are the same, right?
ESI: C1_*alpha()*rho()*GbyNu*Cmu_*k_()
Foundation: C1_*alpha()*rho()*G*epsilon_()/k_()


I'd truly appreciate any clarification.