Deriving SPH - Question about Dissipation
In the DualSPHyiscs wiki I find that;
Where GAMMA is the dissipation term. When I start from the original Navier-Stokes equation I reach this point;
My question is then, I suppose that this GAMMA term in the wiki corresponds to that which I have marked with yellow? (Of course I just need to divide by density as well)
If this is the case, then can anyone explain to me why do we need to use something as artificial viscosity, can we not just evaluate this term marked with yellow directly?
I have had a hard time finding papers starting from the Navier-Stokes eqn., so if somebody knows of a detailed derivation I would be happy to read it.