Tetras, Prims, BL-resolution and element quality

fonzie · November 28, 2009, 10:50

Hello everyone,

I have a question concerning the usage of an unstructured ICEM hybrid mesh in connection with CFX.

I know that I am supposed to use prism elements in order to resolve the BL and I am doing so. The obvious reason is that I need considerably fewer "high-quality" Prisms than I would need if I used Tets. So far so good. My question is: What is the mathematical advantage of a "high-quality" Prism compared to a "low-quality" Tetra?

Both show a large difference between their smallest and largest surface, consequently the control volumes generated by CFX will also do so. Actually I thought the issue would be with the angles between the element surfaces, but since CFX uses shape functions, every element may be regarded as a skewed coordinate system, right? So I cannot see where the inner-element-angles are used ...

The manual says: "... negative influences may be introduced into the discreteziation through finite-element-shape functions, and these influences may grow as geometrical mesh quality deteriorates. ...". I simply do not understand how this introduction works. I guess that there is no easy or short answer to my question. If so, I would also be very grateful for any advice on good literature where I can find an explanation.

Thanks and regards,
Andy

ghorrocks · November 28, 2009, 18:53

There are two main numerical benefits of prism layers. When the flow is aligned with the grid (as it is in a BL mesh) then there is a large flow along the long axis of the element but not much across the element. This means changes in the flow along the long axis are reasonably independent of that across the axis. This is good as the magnitude of these flows are quite different so they are resolved more accurately when the are seperated.

If you use tets in the BL, even high aspect ratio tets, there will be at least one face at a angle to the flow such that tangential and normal flows must be calculated on the same face. The tangential flow is far larger than the normal flow so the normal flow gets swamped out and is difficult to resolve accurately.

The second benefit of prism layers, which is also due to the separate handling of tangential and normal velocities is its reduced numerical dissipation. The angled face on a tet mesh causes a smearing of the BL profile.

Computational Fluid Dynamics by Roache has some good discussion on this issue.

fonzie · November 30, 2009, 04:33

Thank you very much for this reply. That certainly helps a lot !

November 28, 2009, 10:50	Tetras, Prims, BL-resolution and element quality	#1
fonzie New Member Join Date: Mar 2009 Posts: 2 Rep Power: 0	Hello everyone, I have a question concerning the usage of an unstructured ICEM hybrid mesh in connection with CFX. I know that I am supposed to use prism elements in order to resolve the BL and I am doing so. The obvious reason is that I need considerably fewer "high-quality" Prisms than I would need if I used Tets. So far so good. My question is: What is the mathematical advantage of a "high-quality" Prism compared to a "low-quality" Tetra? Both show a large difference between their smallest and largest surface, consequently the control volumes generated by CFX will also do so. Actually I thought the issue would be with the angles between the element surfaces, but since CFX uses shape functions, every element may be regarded as a skewed coordinate system, right? So I cannot see where the inner-element-angles are used ... The manual says: "... negative influences may be introduced into the discreteziation through finite-element-shape functions, and these influences may grow as geometrical mesh quality deteriorates. ...". I simply do not understand how this introduction works. I guess that there is no easy or short answer to my question. If so, I would also be very grateful for any advice on good literature where I can find an explanation. Thanks and regards, Andy

November 30, 2009, 04:33	issue solved - thank you	#3
fonzie New Member Join Date: Mar 2009 Posts: 2 Rep Power: 0	Thank you very much for this reply. That certainly helps a lot !

November 28, 2009, 18:53		#2
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,852 Rep Power: 144	There are two main numerical benefits of prism layers. When the flow is aligned with the grid (as it is in a BL mesh) then there is a large flow along the long axis of the element but not much across the element. This means changes in the flow along the long axis are reasonably independent of that across the axis. This is good as the magnitude of these flows are quite different so they are resolved more accurately when the are seperated. If you use tets in the BL, even high aspect ratio tets, there will be at least one face at a angle to the flow such that tangential and normal flows must be calculated on the same face. The tangential flow is far larger than the normal flow so the normal flow gets swamped out and is difficult to resolve accurately. The second benefit of prism layers, which is also due to the separate handling of tangential and normal velocities is its reduced numerical dissipation. The angled face on a tet mesh causes a smearing of the BL profile. Computational Fluid Dynamics by Roache has some good discussion on this issue.