Boundary condition with value, gradient and constant/source term

Arman_N · January 25, 2022, 16:03

Hello everyone,

I need to implement a boundary condition which is a combination of the value and gradient of a parameter with a constant/source term.
For example, for parameter

the desired equation at boundary is as follows:

$c_{1}\nabla Y + c_{2}Y = c_{3}$

where $c_{1}$ , $c_{2}$ , and $c_{3}$ are constants.

I wanted to know if there is any BC already available in openFoam for this purpose and if not, how can this be achieved.

*PS: I know this can be somehow implemented using the mixed BC when $c_{3} = 0$ , but I need the more general approach.

Any hint is appreciated.

Arman

abhishekmonu96` · February 1, 2022, 12:27

Hi Arman,
You can achieve this by using codeStream. Use codedFixedValue, include necesary libraries and <#include "fvCFD.H"> in the required header files. You can use most of the functions provided in openfoam by this BC.
Here is the link for template:
https://www.openfoam.com/documentati...xed-value.html

Arman_N · February 5, 2022, 08:43

Hi "abhishekmonu96`",

Thanks for your reply. I'm not really familiar with codeStream but I assume it is an efficient way to tweak your way into custom BCs. I will give it a try!

*UPDATE:
After all, I did some more searching and found that apparently, wallHeatTransfer BC does something similar to what I'm looking for, which is itself based on the mixed BC.
Thank to this post, I was able to figure out how it works and apply my own BC.

The mixed BC calculates the value on patch using the following equation:

$Y_{face} = \omega Y_{ref} + (1 - \omega) (Y_{cell} + \delta \nabla Y_{ref})$

where $\omega$ is valueFraction, $Y_{ref}$ is refValue, $Y_{cell}$ is the cell internal value next to face, $\nabla Y_{ref}$ is refGrad, and $\delta$ is the distance between cell face and cell center (=1/deltaCoeffs()).

The main idea is to replace the derivative term with its linear approximation. Therefore, the equation becomes:

$c_{1} (\frac{Y_{face} - Y_{cell}}{\delta}) + c_{2} Y_{face} = c_{3}$

reordering into the mixed BC form gives:

$Y_{face} = (\frac{1}{1+\frac{c_{1}}{\delta c_{2}}}) \frac{c_{3}}{c_{2}} + (\frac{\frac{c_{1}}{\delta c_{2}}}{1+\frac{c_{1}}{\delta c_{2}}}) Y_{cell}$

Therefore, by assuming $\omega = \frac{1}{1+\frac{c_{1}}{\delta c_{2}}}$ , $Y_{ref} = \frac{c_{3}}{c_{2}}$ , and $\nabla Y_{ref} = 0$ , one can implement the desired boundary condition similar to wallHeatTransfer BC.

Cheers,

January 25, 2022, 16:03	Boundary condition with value, gradient and constant/source term	#1
Arman_N New Member Arman N Join Date: Mar 2019 Posts: 13 Rep Power: 7	Hello everyone, I need to implement a boundary condition which is a combination of the value and gradient of a parameter with a constant/source term. For example, for parameter the desired equation at boundary is as follows: $c_{1}\nabla Y + c_{2}Y = c_{3}$ where $c_{1}$ , $c_{2}$ , and $c_{3}$ are constants. I wanted to know if there is any BC already available in openFoam for this purpose and if not, how can this be achieved. *PS: I know this can be somehow implemented using the mixed BC when $c_{3} = 0$ , but I need the more general approach. Any hint is appreciated. Arman

February 1, 2022, 12:27		#2
abhishekmonu96` New Member Join Date: May 2021 Posts: 5 Rep Power: 5	Hi Arman, You can achieve this by using codeStream. Use codedFixedValue, include necesary libraries and <#include "fvCFD.H"> in the required header files. You can use most of the functions provided in openfoam by this BC. Here is the link for template: https://www.openfoam.com/documentati...xed-value.html Arman_N likes this.

February 5, 2022, 08:43	Solved!	#3
Arman_N New Member Arman N Join Date: Mar 2019 Posts: 13 Rep Power: 7	Hi "abhishekmonu96`", Thanks for your reply. I'm not really familiar with codeStream but I assume it is an efficient way to tweak your way into custom BCs. I will give it a try! UPDATE: After all, I did some more searching and found that apparently, wallHeatTransfer* BC does something similar to what I'm looking for, which is itself based on the mixed BC. Thank to this post, I was able to figure out how it works and apply my own BC. The mixed BC calculates the value on patch using the following equation: $Y_{face} = \omega Y_{ref} + (1 - \omega) (Y_{cell} + \delta \nabla Y_{ref})$ where $\omega$ is valueFraction, $Y_{ref}$ is refValue, $Y_{cell}$ is the cell internal value next to face, $\nabla Y_{ref}$ is refGrad, and $\delta$ is the distance between cell face and cell center (=1/deltaCoeffs()). The main idea is to replace the derivative term with its linear approximation. Therefore, the equation becomes: $c_{1} (\frac{Y_{face} - Y_{cell}}{\delta}) + c_{2} Y_{face} = c_{3}$ reordering into the mixed BC form gives: $Y_{face} = (\frac{1}{1+\frac{c_{1}}{\delta c_{2}}}) \frac{c_{3}}{c_{2}} + (\frac{\frac{c_{1}}{\delta c_{2}}}{1+\frac{c_{1}}{\delta c_{2}}}) Y_{cell}$ Therefore, by assuming $\omega = \frac{1}{1+\frac{c_{1}}{\delta c_{2}}}$ , $Y_{ref} = \frac{c_{3}}{c_{2}}$ , and $\nabla Y_{ref} = 0$ , one can implement the desired boundary condition similar to wallHeatTransfer BC. Cheers,

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