Anybody knows when to use conservative form for the advection term or non-conservative form by using finite difference method? For imcomprssible flow, it should be no different, am I right?

Thanks,

Jinfeng

Even in incompressible flow, for the mass conservation conservative form is prefered.

I'd say it all depend on your criteria for accuracy. If conservation is a criteria then the answer is most likely to use conservation form. There are non-conservative methods that yield space derivatives with smaller truncation error if that is a criteria.

Also it should be noted that although a method is conservative it does not necessarily imply accuracy. For instance, you can have an unstable solution that is still conservative.

/Y

I agree with you on that comment.

For example, high order Godunov type upwinding method and some ENO type are used, non-conservative form is naturally used.

But for the transport of density or volume-fraction, still conservative form is used to preserve conservation of those quantities.

Well, I think the choice depends on the problems. For compressible flows conservative forms finite volume schemes is the safest choice. Even using high order Godunov. Although with high order schemes it is a question of flavours. MPWENO, entropy-splitting, flux and slope limiters..you name it. In turbulence applications, some schems will dissipate more than others, destroying part of the information, other will dissipate less and therefore oscillate.

However, one question I would like to ask, what happened with the advection term in a non conservative equation?, i. e.

rdQ/dt + rvdQ/dx where v is a velocity conditioned on some variable, Q is a conditional scalar and r a conditional density, therefore dr/dt + d(rv)/dx is NOT zero

Which kind of discretization schemes will be suitable for this term?.