[MissCFD]

In CFX-Solver theroy guide (chapter 11), it is say that the integration points are located at the center of each surface segment within an element.

It's not clear for me the location of these integration points. Can somebody please explain it to me ?

I read somewhere that the integration points are located at the center of finite volume's faces. For me, it's wrong but i would like the confirmation.

[Opaque]

That interpretation is correct in the isoparametric representation of the element.

Why do you think is wrong ?

[MissCFD]

What is an isoparametric representation of the element ?



For me, if I think only with an 2D mesh hexa, the center of each surface segment within an element doesn’t correspond to the center of finite volume's faces, no ?.

Originally Posted by Opaque

That interpretation is correct in the isoparametric representation of the element.

Why do you think is wrong ?

[Opaque]

In a 2D case with only quad elements, a control volume shares 4 quad elements. Within an element, the faces of the control volume starts at the midpoint of the edges of the element towards the center of the element; therefore, two segments. The integration points is located at the midpoint of each segment, that means for the complete control volume you get 8 integration points.

You can look in the literature for is also called the mesh-dual. CFX solves the equations in the mesh-dual where the control volumes are polyhedrals.

http://www.arc.vt.edu/ansys_help/cfx_thry/i1311648.html

[MissCFD]

Thank you for your explanation.



So with your example, we are agree that the integration points isn’t located at the center of the of the control volum ?



It’s a complete control volum or a complete face of control volum which give 8 integration points ? For me, it’s the last proposition but maybe there is something else that I don’t see it yet.

Originally Posted by Opaque

In a 2D case with only quad elements, a control volume shares 4 quad elements. Within an element, the faces of the control volume starts at the midpoint of the edges of the element towards the center of the element; therefore, two segments. The integration points is located at the midpoint of each segment, that means for the complete control volume you get 8 integration points.

You can look in the literature for is also called the mesh-dual. CFX solves the equations in the mesh-dual where the control volumes are polyhedrals.

http://www.arc.vt.edu/ansys_help/cfx_thry/i1311648.html

[Opaque]

You are confusing face integration points with the control volume mean value point. Integration points are to be used to evaluate surface fluxes.

Perhaps you are mixing cell-vertex discretization with cell-center discretization ?

[MissCFD]

Can you recapitulate please ?

Used to evaluate surface fluxes, the integration points are located at the center of segment joining the centers of the edge and element centers.

1) So in the 2D case mentioned above, we are 8 integrations points for a complete volume finite (2D). In the 3D case, it gave 8 * 6 faces = 48 integrations points, is that right ?

2) So, the integration points aren't located at the center of finite volume's faces as I could read it.

Originally Posted by Opaque

You are confusing face integration points with the control volume mean value point. Integration points are to be used to evaluate surface fluxes.

Perhaps you are mixing cell-vertex discretization with cell-center discretization ?

[Opaque]

1) So in the 2D case mentioned above, we are 8 integrations points for a complete volume finite (2D). In the 3D case, it gave 8 * 6 faces = 48 integrations points, is that right ?

Your extrapolation to 3D seems incorrect. There will be 3 faces within each element sector with an integration point in the middle of each face; therefore, the total number of integration points at control volume faces equal 8 * 3 = 24.

A 3D quad face reduces to a line face in 2D, the i.p. at the middle of the quad face collapses to the midpoint of the edge.

[MissCFD]

I'm sorry but I don't understand why * 3 ? I think that I don't see the three faces within each element sector ...

On the picture, I draw the 8 integration points. For me, the grid area correspond to one face (seen from above) of the control volume.
Should I imagine an extrusion of this grid area in the direction perpendicular at this view ?

Originally Posted by Opaque

Your extrapolation to 3D seems incorrect. There will be 3 faces within each element sector with an integration point in the middle of each face; therefore, the total number of integration points at control volume faces equal 8 * 3 = 24.

A 3D quad face reduces to a line face in 2D, the i.p. at the middle of the quad face collapses to the midpoint of the edge.

[Opaque]

An element sector is always a hex sub-element; therefore, 6 faces. Of those 6 , 3 faces are interior faces within the control volume and shared with the neighbor control volume element sectors.

When you evaluate the surface fluxes, the interior fluxes cancel each other (conservation); therefore, those faces do not count (though you can keep them in the topology if you want)

Then, you get 8 hex-octants with 3 external faces each = 24 integration points.

[MissCFD]

Thank you very much; it seems clearer in my mind but not completely yet …



To be sure to visualize your comments, I join two pictures.


On the first, the green contour shows an element sector (6 faces). On the second, the blue lines show interior faces within the control volume, I can only make out two and so four faces are shared with the neighbor control volume element sectors. What is wrong in my way of thinking?

Originally Posted by Opaque

An element sector is always a hex sub-element; therefore, 6 faces. Of those 6 , 3 faces are interior faces within the control volume and shared with the neighbor control volume element sectors.

When you evaluate the surface fluxes, the interior fluxes cancel each other (conservation); therefore, those faces do not count (though you can keep them in the topology if you want)

Then, you get 8 hex-octants with 3 external faces each = 24 integration points.

[Opaque]

You are drawing 2D, and try to understand 3D w/o spatial visualization. My advice is to get paper and scissors and built a set of 8 cubes.

Use the cubes for control volume sector, and join them. You will see which are the shared faces between the sectors.

[MissCFD]

Yes, thank you very much. I realized my mistake after my post.

By contrast, can you explain me the general approach of CFX solver to solve equations ?

I understand that the initialization allows to give an initial pressure and an initial velocity field on the nodes of mesh, throughout the domain. But what happens at the following iteration ? We are news values on the node of mesh and we interpolate these values at integration points to solve N-S equation and continuity ?

Originally Posted by Opaque

You are drawing 2D, and try to understand 3D w/o spatial visualization. My advice is to get paper and scissors and built a set of 8 cubes.

Use the cubes for control volume sector, and join them. You will see which are the shared faces between the sectors.