[gns4566]

Dear all

I'm solving with the problem with 2D axisymmetric NS.

For my research, I'm studying with the book the name

"Computational Fluid Dynamics: Principles and Applications" written by Blazek.



From here, my question is why should I have to muliply radius with (Convective flux - viscous flux )

Can anyone help me what is the exact equation for 2D axisymmetric navier-stokes equation for FVM?

As I know, symmetry is related to source term. So I think the flux term for navier-stokes equations with symmetry should be same as normal equation.

Please help me

Thank you for reading.!

[aerosayan]

That's probably the surface normal or radial vector in the cylindrical co-ordinate system.

Cylindrical formulation is necessary for things like jet turbine simulations or plasma tokomak simulations.

I have only studied about solving NS equations in cartesian co-ordinate system and we multiply the fluxes with the cell surface area and the direction vector. That's something like (F-G).nds.

The r is probably not just the radius, but the radius vector. That is, how much far the point is from the center, and what's the vector direction of this point.

It's better if you understood the physical meaning of the equation. The equation signifies what magnitude of flux is moving into or out of the control volume. The n is the surface normal and thus signifies the direction of the flux.

In cylindrical co-ordinates you have something similar. Though I don't have much experience in solving for cylindrical co-ordinates, so I can't explain it to you in much detail.

[FMDenaro]

Originally Posted by gns4566

Dear all

I'm solving with the problem with 2D axisymmetric NS.

For my research, I'm studying with the book the name

"Computational Fluid Dynamics: Principles and Applications" written by Blazek.



From here, my question is why should I have to muliply radius with (Convective flux - viscous flux )

Can anyone help me what is the exact equation for 2D axisymmetric navier-stokes equation for FVM?

As I know, symmetry is related to source term. So I think the flux term for navier-stokes equations with symmetry should be same as normal equation.

Please help me

Thank you for reading.!

I think the last sentence should address the answer. You should start considering the elementary volume dOmega=r dtheta dr dz.

I would assume in the textbook that r dS is the elementary surface.
However, I should check in the book some notation Blazek adopted...

[gns4566]

Originally Posted by aerosayan

That's probably the surface normal or radial vector in the cylindrical co-ordinate system.

Cylindrical formulation is necessary for things like jet turbine simulations or plasma tokomak simulations.

I have only studied about solving NS equations in cartesian co-ordinate system and we multiply the fluxes with the cell surface area and the direction vector. That's something like (F-G).nds.

The r is probably not just the radius, but the radius vector. That is, how much far the point is from the center, and what's the vector direction of this point.

It's better if you understood the physical meaning of the equation. The equation signifies what magnitude of flux is moving into or out of the control volume. The n is the surface normal and thus signifies the direction of the flux.

In cylindrical co-ordinates you have something similar. Though I don't have much experience in solving for cylindrical co-ordinates, so I can't explain it to you in much detail.

Thank you very muhc for your reply. I got the point what you said.