That's basically identical to summing up all tetrahedral pyramids from any three surface points and a common fourth point in the middle. I've not yet seen it from that angle though. Very interesting, thanks for the video!
19:10 - Mathematically speaking, I think that even if you calculate coordinates of the face's centroid from any other origin (for example global origin), you should get the same result of the calculated volume of the cell. ;)
I am your fan and notice maybe a problem at 24:13. Should the Xf of left surface to be (-1,0) instead of (-1,1) when the Xf of right surface is (1,0)? Please correct me if I was wrong. Thanks!
Note that the midpoint rule evaluation is somewhat tricky for faces that are non-planar. In fact the geometric definition of non-planar faces is itself ambiguous.
Many Thanks to your efforts. Very helpful videos , helping to make complex things far more easier . I really appreciate if you could make a small video that sums up the whole story. I have a general question, first we solve the quations after putting it in matrix form this give us the centroid values of the cell , then we use these values to bring the face values then we do what , after this stage?
After you have solved the matrix equations and have the centroid values and face values (normally this requires iteration and takes a long time to solve) then you have your solution. You are finished! You can move on to the post processor and make plots of your solution
Hello Aidan, For a general 3D arbitrary shaped cell, equation-21 provides an expression to calculate cell-volume V_p. However, how does a CFD code calculate a face normal vector pointing outward (ncap_f) and area of any face? As there is no parametric expression for a face (surface) here, how does it calculate these quantities? Can you please briefly discuss on it or maybe point to any available literature? Thank you
The book 'Notes on Computational Fluid Dynamics: General principles' by Greenshields and Weller, gives a good description. You can also get it for free if you read the online version ☺️
If the faces of some of the cells are inverted or colliding with other cells, then the mesh generator may calculate a negative cell volume. This is really just an indication that your mesh is invalid and needs to be fixed, as the CFD code won't run with a negative cell volume
Thanks to your content, it is really amazing. However, if you don't mind, can you please adjust your own view for upcoming videos? Sometimes, it is hiding the slide contents :)
![[CFD] Green-Gauss Cell-Based and Node-Based Gradient Schemes](http://i.ytimg.com/vi/oeA1Bg9GqQQ/mqdefault.jpg)
![[CFD] Green-Gauss Cell-Based and Node-Based Gradient Schemes](/img/tr.png)
![[CFD] Mesh Non-Orthogonality 2: The Over-Relaxed Approach](http://i.ytimg.com/vi/yU7r8mYK3bs/mqdefault.jpg)
![The Most Useful Curve in Mathematics [Logarithms]](/img/1.gif)
Never understood any concept of CFD better before until after watching these videos!
You have made CFD calculation to become easier. Thank you very much 😀😀😀😀
Very very good. You have been making CFD easier to understand for everyone.
The decomposition with the graphic reminder to work from cell center is very helpful and core to many CAE methods. We’ll done.
Super clear and useful lecture. Great type of content, looking foreward for more.
A very interesting formula/algorithm! Not only just to use for making your own CFD code, but very interesting in general!
That's basically identical to summing up all tetrahedral pyramids from any three surface points and a common fourth point in the middle. I've not yet seen it from that angle though. Very interesting, thanks for the video!
Yep!
maybe I'm incorrect but in the 1st retangle in 2D Worked example, the left face I was wondering if the dot product would be: 0.5(-1,0)(-1,0)1
Likewise!
This is what I get as well, that way the final area adds up to 2 as expected.
Looks like this is a typo. Thanks for pointing this out everyone 😊
Really a quick, easy and interesting video of how the Gauss theorem is used here :)
19:10 - Mathematically speaking, I think that even if you calculate coordinates of the face's centroid from any other origin (for example global origin), you should get the same result of the calculated volume of the cell. ;)
You are probably right. I couldnt get it to work with the global origin though 🤦♂️
@@fluidmechanics101 The difference between the two origins is a fixed vector, and the closed surface integral of any fixed vector is definitely zero.
As always, found it very interesting and useful. :) I think from the equation (32), the surface normal for the left face would be (-1,0) .
Yep well spotted!
I am your fan and notice maybe a problem at 24:13. Should the Xf of left surface to be (-1,0) instead of (-1,1) when the Xf of right surface is (1,0)? Please correct me if I was wrong. Thanks!
I agree indeed.
Note that the midpoint rule evaluation is somewhat tricky for faces that are non-planar. In fact the geometric definition of non-planar faces is itself ambiguous.
sir you have explain in very excellent way
Useful and interesting.
Many Thanks to your efforts. Very helpful videos , helping to make complex things far more easier . I really appreciate if you could make a small video that sums up the whole story. I have a general question, first we solve the quations after putting it in matrix form this give us the centroid values of the cell , then we use these values to bring the face values then we do what , after this stage?
After you have solved the matrix equations and have the centroid values and face values (normally this requires iteration and takes a long time to solve) then you have your solution. You are finished! You can move on to the post processor and make plots of your solution
Interesting concept . Thanks a lot
Very useful
Thanks for uploading such detailed videos.. I have a request can you please upload regarding solidification and melting module?
Solidification and melting is quite difficult! I am planning to do a vid in future but not quite yet 😊
Fluid Mechanics 101 thank you and keep posting.. and
Very good and valuable presentation. 👍
Hello Aidan,
For a general 3D arbitrary shaped cell, equation-21 provides an expression to calculate cell-volume V_p. However, how does a CFD code calculate a face normal vector pointing outward (ncap_f) and area of any face? As there is no parametric expression for a face (surface) here, how does it calculate these quantities? Can you please briefly discuss on it or maybe point to any available literature? Thank you
The book 'Notes on Computational Fluid Dynamics: General principles' by Greenshields and Weller, gives a good description. You can also get it for free if you read the online version ☺️
Thank you Aidan, I will have a look at it. 😀
Thanks for your video. U said that normal vector is always pointing out of the cell and Vp is positive. So why do we meet negative cell volume ?
If the faces of some of the cells are inverted or colliding with other cells, then the mesh generator may calculate a negative cell volume. This is really just an indication that your mesh is invalid and needs to be fixed, as the CFD code won't run with a negative cell volume
@@fluidmechanics101 Thanks a lot
Will you be doing an explanation of the k-omega model as you did for k-epsilon?
Oh sorry, I was being stupid, you have already done it here:
ruclips.net/video/myv-ityFnS4/видео.html
Thanks!
Beautiful. Could you please do a tutorial on computing hydrodynamic potentials of onshore structure using the panel method?
Thanks to your content, it is really amazing. However, if you don't mind, can you please adjust your own view for upcoming videos? Sometimes, it is hiding the slide contents :)
I am waiting. :)...thanks for the upload.
“All the flow variables are stored at the cell centroids”
And the normal vector of left should be (-1,0)