I am trying to add an extra stress term to Navier Stokes, as I understood I need to use weak contribution. But I don't know how exactly enter the weak form in NS equation.
let's say you have the momentum equation and the constraint
d_t v + div T - f = 0
div v = 0
where v is a vector quantity (velocity), d_t is the time-derivative, T is a flux (second order tensor, i.e. stress tensor) and f is a vector source term (a force),
the weak form (lagrangian) for this system of PDE is
W1 = d_t v . u - grad u : T - f . v
W2 = q div v
in comsol "language" you need to put these equations in two physics. One has three unknowns (the three velocity components) and the other has one unknown (that is the pressure p). It would be better to have for the velocity a Lagrange-2 discretization and for the pressure a Lagrange-1 discretization (I mean polynomial order). Then you have four contributions