Convection-Diffusion with implicit source
 

Hi Foamers,
I need to solve this convection-diffusion problem:

d(ut_i)/dt + d(U_j ut_i) / dx_j - nu d2(ut_i) / dx_j2 = - ut_j d(U_i) / dx_j

where ut is my variable, U is a velocity field known.

I implemented it like this:

fvVectorMatrix utEqn
(
fvm::ddt(ut)
+ fvm::div(phi, ut)
- fvm::laplacian(nu, ut)
==
- fvc::div(phiUt, U)
);

utEqn.relax();
utEqn.solve();

but, I prefer to introduce - fvc::div(phiUtf, U) in an implicit way.
When I try to do - fvm::div(phiUtf, U), it gives me error.
What can be a good way to do it?
Thank you,
Ivan