What are the advantages of using the strong conservation form of the Navier-Stokes equations ? . I would like to know the advantages it offers over other forms in different areas of application.

I discretize the equations by the FVM method, and the strong conservation form gives a very compact form.

Thanks for your answer.I'm looking at it from mathematical point of view.I'm just curious if there is any mathematical advantage in formulating in the strong conservation form.

In my concerns, the conservative form is strongly encouraged to capture the shock structure exactly. If your initial conditions have discontinuities, we'd rather use the conservative form of N.S equations. That's very general and extensively mentioned comments in the community of the cfd research.

Good luck for your work.

Conservation is required to model the process very accurately. Simply look at the convection term of NS. (rho UU )

Now given a grid

-U-C-D-

Upsteam U, C Cell , D downstream.

Across the faces rhoU (flux) conserved and discretizing the term Del. (rho UU) as such preserves conservation of momentum

i.e., rhoU U in faces between U and C = rhoU U across faces C-D

However, in non-conservation form

Del.(rhoU U ) = U.del (rhoU)

The computed Uf where f between C-D results in Uf . del (rhoU)(computed across the faces) not equal across the faces across C-U !!

Strong Conservation form is required to maintain balance of conserved quantities.

Using a non-conservation form (expanding the compact form) for easy representation in a FV method leads to incorrect computation of the fluxes leading to large errors!

As posted before, this would be critical between getting a right location of the shock and totally misjudging the position and strength of a shock front.

Similar problems are magnified in combination with other terms in the NS equations.

FVM method very well suits the Conservation property and is always preferred !

CFDtoy

"Using a non-conservation form (expanding the compact form) for easy representation in a FV method leads to incorrect computation of the fluxes leading to large errors!"

That's not actually true - it depends upon the problem that you are solving and the norm you calculate your error in. There's an example of this in Anderson's book where it is shown that the nonconservative form can be more accurate (pointwise) than the conservative form.