[arungovindneelan]

While deriving integral form of NS equation, we use Gauss divergence*theorem to convert volume integral to surface integral. Why we are doing this?

Divergence term has derivative calculation. In high-speed flow there will be discontinuity in flux, so calculating derivative is meaningless. If this is a reason resulting*form of NS equation after divergence theorem also looks like equivalent*finite difference form of derivative calculation.

We can evaluate flux across boundary easily if we use divergence theorem. Using that we can ensure conservativeness of flux. But conservativeness of flux does not ensure conservativeness*of mass, momentum etc. for transient case (because fluxes are discontinuous in transient stage but mass, momentum etc. are not) *. Because conservativeness*is based on combined spatial and temporal parts. I believe only doing spatial will not ensure conservativeness except steady state case.

Why we use Gauss divergence theorem in Weak form of Navier-Stokes equation? - ResearchGate. Available from: https://www.researchgate.net/post/Wh...366d4b5f24bc51 [accessed Sep 27, 2016].