Is it possible to write the conservative form of Navier-stokes equation in cylindrical coordinates? Almost all texts I have referred (Frank M. White, Kundu & Cohen,G.Batchelor) have it in non-conservative form. Can anyone give me the conservative form of Navier-stokes equations in cylindrical coordinates or point to a text that has it?
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I think you should take a look at this answer about Conservation vs non-conservation forms of conservation equations. And as Zero stated in the comments, a quick Google search can give you the answer. You also seem to have asked the same question on cfd-online forum. There is also some information in there.
In the last link, a nice answer expressed the physical meaning of the difference :
The conservative form derives from expressing the conservation equations in a divergence form, i.e. the equations have the form of local time rate of change + divergence of flux = source terms. The non-conservative form is a form of the equations that is not expressible in this form. One of the principle advantages to the the conservative form is that once the equations are discretized, the flux terms "telescope", that is if you sum the fluxes into and out of a row of cells, the intercell fluxes cancel and the net flux is just the flux out of one end of the row - flux in the other end.
To answer the question, yes, it is possible. Conservative or non-conservative formulation of Navier-Stokes equations are linked. As the cited answers state, the difference will only appear when you try to discretize the equations. Thus, if you have something, referred as being a non conservative formulation, like $$\rho\frac{\partial u}{\partial t} + u\frac{\partial \rho}{\partial t}$$ in your equation, you can rewrite it as $$\frac{\partial \rho u}{\partial t}$$ and get back to the conservative form. If your problem is that $\rho$ has been extracted from the partial derivation, you can easily put it back inside by manipulating the terms, before any discretization, and obtain the conservative form.
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