Thank you Max for your help. I was able to mesh my geometry. Just for curiosity, Is there any way to mesh Face 2 by Quad map instead of Quad pave?, because it can significantly improve my calculation downstream pipe (volume 2). I was only able to mesh Face 1 with Quad map (since it is annulus face).

yes with o-grid

Dear Max,

I tried to use O-ring method based on another Thread that you suggested, here is the procedure which, unfortunately, failed:

First, I created a cube inside a circle, I chose four vertexes on the circle's edges, connect corner of cube to four vertexes on circle. I separated circle edges into four edges.now, I have five faces, including cube. Idid the same on the other face wich has a larger diameter at contraction point. When I reapet the procedure, as you suggested before, to create a surface inside upstream volume by edges, an error occurred. I attached to you geometry. What should I do in this case.

alright I understand you cannot create the surfaces parallel to the cylinder axis, right?
Did you split the cylinder surface (smallest diameter of the annulus volume)?

Exactly, I cannot create surface from edges parallel to the pipe axis. I also splited small circle into four arc edges. Now in the small circle, I have 5 faces, including one cube.

As I mentionned, you need to split the cylinder surface with circle's vertices
Attachment 53450

As I told you, I have separated the circle from vertexes. Still not working.

how did you create the lines parallel to the axis?

I created two cubes inside circles. I connected vertexes on first and second circles. Also, each vertex on cube to similar one in the second cube. I simply used create edges from vertexes. But, the problem is that when I want to create surface from edges.

If you "simple" create Lines like that; then you will not be able to Split the Volume. That s Why I suggested to Split the surface with vertex


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Here is the procedure that I did:

As you told, I created four vertexes on circle, then, I have splited face (circle) from four vertexes. So, the result would be a cube inside circle. Eventually, I have 5 faces, see pic 1. I did the same for the second circle (see pic 2).
I have linked each vertex on the first circle to the similar one on the second circle (see pic 3). I tried to create face from edges, but still unsuccessful (see pic 4). Something else that I should know?

No,
your splits are wrong.
What you proposed at #23 was good.
You only didn't get my point regarding the splits on the cylinder surface.
For that I post a picture: I split the blue surface with both vertices (red)
Attachment 53526
Attachment 53525

Excuse me Max, but I do not think you get my problem. I understand that I should split the blue surface from red vertexes in your shared photo. My problem is not to separate two volumes. The big problem is :
When I created four vertexes on small circles in both sides (circles 1 and 2), then created edges 1,2,3,4.
I created surfaces from edge 1, edge 3, edge 5, and edge 9. I created also surface from edges 3, 4, edge 6, and 10 and so on (see picture 1). I separated volume from created surfaces to create two volumes. So, the step you suggested is not needed. Question: How can I make a Quad map in picture 3?

you cannot because this surface is not meshable with map.
You didn't split it as it should be.
The 4 corners of your square don't have to lie on the circle.
I previously mentionned you that this split was not correct.
See your post #23, where you displayed your previous split (and it was good)