Use Finite Volume Method (FVM). Good luck

 The following methods can be performed in order to solve the Navier-Stokes equations

 Discretization schemes for the Navier-Stokes equations

 Pressure-based approach

 Density-based approach

 Convergence acceleration

 Periodic Flows

 Unsteady Flows

It depends on the context of your study...

Give us more details about your problem? 

Try finite differences in

Fluid Flow Phenomena-A Numerical Toolkit_-_Paolo Orlandi

The book comes with codes in fortran for 3D transient, in cilindrical coordinates, chp 7, 10 and 11.

Finite Differences or Finite Volume could be applied.

For basic introduction about these methods you can refer to some books for Computational Fluid Dynamics such as from Versteeg H., Malalasekra W.

I agree with Mahesa, the common methods are finite volume and finite differences, but it is really depends on what you are doing.  

If your flow is axisymmetric or axisymmetric with swirl, it can be benefical to use cylindrical coordinates. If this is not the case, I would recommend to stick to x,y,z.

Are you trying to write your own CFD-solver or do you want to use something ready to go?

Thank you all. My aim is to incorporate magnetic field on Navier-Stokes equations in cylindrical geometry. Reason?,   Alot of works have been carried out in one-dimensional form.

You want to write your own code or just used the SW available already?

finite volume method with upwind differencing scheme is the better way ....

@Bensayah, please can you help me with more details on how to use either?. thank you