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implicit - scalar product source term in momentum equation

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Old   October 28, 2014, 15:57
Default implicit - scalar product source term in momentum equation
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vinch
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Dear all,
I would like to add an implicit source term to the momentum equation of the fluid solver (in the BuoyantBoussinesqPimpleFoam framework.
I read on this forum the following thread :
Adding implicit source term to momentum equation
where the user needed to add a non linear term. The expression of my source term is different and the solutions given were not satisfying I guess, so I think this is worth having a new thread.

I would like to add a source term looking like this :
F = a (G . U) K
where the capital quantities are vectors. U is the unknown velocity.
In the code, I used the following lines :

Code:
    fvVectorMatrix UEqn
    (
        fvm::ddt(U)
      + fvm::div(phi, U)
      + turbulence->divDevReff(U)
      + a * (G & U) * K
      ==
      fvOptions(U)
    );
but this way, the force is fully explicit.
I can't use the fvm::Sp() method since the second argument required is the variable being implicit, and it expects a vector, not the result of a scalar product.

My question is thus, is there a way to write this as a fully implicit source term ?
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