Folks:

I'm deriving the SIMPLE axial and radial momentum equations for an axisymmetric pipe flow problem. It's been some years since I worked with SIMPLE, and I've lost all my derivation notes. My question is the following:

Due to the staggered grid control volumes, is the axial velocity considered zero in the radial control volume, and the radial velocity zero in the axial control volume? Or, do you interpolate adjacent axial velocities to the center of the eastern and western borders of the radial control volume to integrate the axial transport of radial velocity? I'm ending up with D.nb components for the eastern and western neighbors, but no F.nb components in my coefficients.

Please advise if I'm making a common mistake. I reorganized the equation from the conservative form to the flux-convection form, but then I have problems with integration because of a radial term in the denominator.

If there is no direct advice, can anyone send me the discretization equations for SIMPLE in cylindrical equations? Any assistance would be greatly appreciated.

Thanks in advance, TerraVici

i work resentlly in the laminar mixed convection in the entrance region of semicircular duct so i work with the SIMPLER and finite volume method .

i did not understand your equations well but if you want think about discretization i will help

i am from libya you

[amir2920]

Hello

could you please send me discretization of momentum and energy equation in cylindrical coordinate or a paper that contains this? Thank you in advance.

[amir2920]

Hello

could you please send me discretization of momentum and energy equation in cylindrical coordinate or a paper that contains this? Thank you in advance. my email is: amir2920@gmail.com

[hamed_3439]

hi friends.i'm trying to find the descritized form of navier stokes eq.(momentum and energy) with stream-vorticity notations in cylindrical coordinates.thank you so much if you can help.
best regards