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Clarification needed for zero-flux boundary condition type

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Old   February 26, 2013, 21:07
Default Clarification needed for zero-flux boundary condition type
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Hi folks!

I believe my question is generic to any of CFD software so I decided to put it in here.

I have a really simple question that I cannot get it out of my head, regarding the zero flux boundary condition...

For example, if I have a flow in a simple straight pipe.

I would like to assign some BC's to my computational domain and I understand the velocity inlet BC, outlet BC, etc. I understand that the velocity, mass flux, temperature, pressure, etc. are specified with a constant value. (Dirichlet condition?)

However, when it comes to the zero flux (Neumann condition?) for the remaining variables, referring to the textbooks and published paper, everyone seems to mention the word "zero flux" and give a mathematical expression of, like, dX/dn = 0 (where X is arbitrary variable and n is the normal vector to the surface)

How does a gradient of an arbitrary variable (dX/dn) relate to a zero flux? I do not quite understand what is going on here. Zero flux means there is no flow of X across the face, doesn't it? But, a zero gradient of something, from my understanding, only means there is no change in the variable X in a particular direction which is normal to the surface in this case?

Could you please clarify my question?




Cheers,

pchoopanya
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Old   February 27, 2013, 06:38
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Filippo Maria Denaro
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Quote:
Originally Posted by pchoopanya View Post
Hi folks!

I believe my question is generic to any of CFD software so I decided to put it in here.

I have a really simple question that I cannot get it out of my head, regarding the zero flux boundary condition...

For example, if I have a flow in a simple straight pipe.

I would like to assign some BC's to my computational domain and I understand the velocity inlet BC, outlet BC, etc. I understand that the velocity, mass flux, temperature, pressure, etc. are specified with a constant value. (Dirichlet condition?)

However, when it comes to the zero flux (Neumann condition?) for the remaining variables, referring to the textbooks and published paper, everyone seems to mention the word "zero flux" and give a mathematical expression of, like, dX/dn = 0 (where X is arbitrary variable and n is the normal vector to the surface)

How does a gradient of an arbitrary variable (dX/dn) relate to a zero flux? I do not quite understand what is going on here. Zero flux means there is no flow of X across the face, doesn't it? But, a zero gradient of something, from my understanding, only means there is no change in the variable X in a particular direction which is normal to the surface in this case?

Could you please clarify my question?




Cheers,

pchoopanya

for example, see the Fourier flux q = - k Grad T at an adiabatic wall. Then q =0 implies dT/dn = 0. Hence, you have to discretize the zero normal derivative and computing your wall temperature that ensure the condition q=0
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Old   March 15, 2013, 17:48
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thank you so much for your comment
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Old   March 16, 2013, 06:22
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Quote:
Originally Posted by pchoopanya View Post
Hi folks!

I believe my question is generic to any of CFD software so I decided to put it in here.

I have a really simple question that I cannot get it out of my head, regarding the zero flux boundary condition...

For example, if I have a flow in a simple straight pipe.

I would like to assign some BC's to my computational domain and I understand the velocity inlet BC, outlet BC, etc. I understand that the velocity, mass flux, temperature, pressure, etc. are specified with a constant value. (Dirichlet condition?)

However, when it comes to the zero flux (Neumann condition?) for the remaining variables, referring to the textbooks and published paper, everyone seems to mention the word "zero flux" and give a mathematical expression of, like, dX/dn = 0 (where X is arbitrary variable and n is the normal vector to the surface)

How does a gradient of an arbitrary variable (dX/dn) relate to a zero flux? I do not quite understand what is going on here. Zero flux means there is no flow of X across the face, doesn't it? But, a zero gradient of something, from my understanding, only means there is no change in the variable X in a particular direction which is normal to the surface in this case?

Could you please clarify my question?




Cheers,

pchoopanya

I think the zero flux condition usually (always?) is followed by a zero normal velocity condition as well.

So in this case we have zero diffusive flux across the boundary and the zero normal velocity condition should ensure zero convective flux across the boundary.
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