[CpCaniggia]

Hello everyone,
I am solving a passive vector equation, along with the Navier-Stokes equations. There is a source term related to the main variable (AU & fvc::grad(U)). How can I treat it in an implicit way? The code is as follows,

fvVectorMatrix AUEqn
(
fvm::ddt(AU)
+ fvm::div(phi, AU)
- fvm::laplacian(PrRa_12, AU)
==
- AU & fvc::grad(U)
);

AUEqn.relax();

if (momentumPredictor)
{
solve
(
AUEqn == Arhok*g - fvc::grad(Ap)
);
}

In the present code, "AU & fvc::grad(U)" is treated explicitly. However, the solution is unstable. So I wonder if there is any method to treat it implicitly.

From OpenFoam manual I know that the source term can be solved implicitly by fvm::SuSp(rho , AU). However, rho here must be volScalarField while fvc::grad(U)) in my equation is a volTensorField.

Thank you!