May I suggest you tell each other WHAT you are conserving!

From previous discussions I know that Frederic (LES/DNS community) is referring to several quantities that are of only minor interest to RANS developers. Sebastien (RANS community?) appears to be taking the traditional RANS view of conservation.

To stick in my tupence worth. You can generally arrange the differencing to conserve anything you want so long as you are prepared to drop the consevation of other quantities and, often, drop the order of accuracy.

Thanks andy for your intervention,

Well i'm talking about the conservation of mass momentum and kinetic energy. The staggered as well as the collocated will conserve both mass and momentum. The staggered is also KE conservative, only on uniform mesh, and the convective operator are non-KE conservative on non-uniform meshes, making the scheme non fully conservative on non-uniform meshes. (Cf Vasilyev) The collocated, no matter what, has an error in the pressure term that scale like O(Dt^n, Dx^m). (Cf. Morinishi et al.)

I sincerely advice people to read the two references i gave earlier. Then no more confusions will occur.

sincerely,

Frederic Felten

This is a further clarification of Frederic explanation (the essence of the papers he was talking about).

Most incompressible flow solver use only the continuity and the momentum equations. The energy equation in the incompressible, constant density case is redundant since it can be derived from the continuity and the momentum equations. However, if one tried the same with the discrete equations (i.e., derive the discrete kinetic energy equation from the discrete continuity and the momentum equations), you would end up with a non-conservation form of the kinetic energy equation (though the conservation equations for mass and momentum are themselves fully conservative).

So, a way of spatial discretization for the mass and momentum equations that would enable the derivation of a discretely conservative energy equation is discussed in the paper.

I am not sure that the concepts in this paper can be applied to variable density or fully compressible flows. Also the use of finite-differences is limited in most complex geometries.

Thank you very much Kalyan for this clarification. In addition, these two papers are clearly limited to incompressible flows. For complex geometries, the collocated arrangement, has been prefered by several groups, basing their choice on the relatively simpler implementation (same control volume, geometrical quantites,...Cf Peric, PhD Thesis, University of London, 1985.)

Sincerely,

Frederic Felten.