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What is the name of the formulation for flows with sliding meshes? |
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January 12, 2024, 14:02 |
What is the name of the formulation for flows with sliding meshes?
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#1 |
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ONESP-RO
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Hello,
For typical static meshes, the Navier stokes equations are written in an Eulerian formulation. But I am not sure about meshes that have some parts that are rotating which are usually modeled using the sliding mesh technique. Example: Below is an example of a domain used to simulate the flow around a rotating rectangle object. 1) What is the forumlation name for such simulations? It is certainly not an Eulerian formulation because the inner region is rotating. On the other hand it is not like a Lagrangian formulation either. Any help is very much appreciated. Kind regards ONESP-RO
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January 12, 2024, 14:53 |
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#2 |
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Filippo Maria Denaro
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Have a look to "Chimera methods"
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January 12, 2024, 15:02 |
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#3 |
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Thank you for your reply.
I know a little bit about overset meshes but I am interested in formulation name for sliding meshes. Is it the same as overset meshes? I have checked some resources but they are heavy on maths beyond what I could understand.
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January 12, 2024, 16:59 |
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#4 |
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Lucky
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We just call it moving mesh.
Actually it is still Eulerian because sliding interface is what enables the grid to move in-sync with the motion of the boundaries and it is the same Eulerian equations just with a non-constant mesh. The sliding mesh is the only "new" technique at the mesh interface between stationary and moving parts and it effectively only a BC. The same is true when you have deforming boundaries as long as the grid morphs with the boundary. For these cases, we like to call them dynamic meshes because it requires a re-gridding every time-step whereas the sliding mesh does not require re-gridding. Both are Eulerian. |
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January 14, 2024, 00:41 |
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#5 | |
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Quote:
Eulerian meshes,by definition, are fixed meshes and have no moving vertices. After delving a little bit in literature I found that the formulation used for sliding meshes is known as Arbitrary-Lagrangian-Eulerian (ALE). Kind regards
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January 14, 2024, 01:11 |
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#6 |
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Eulerian reference frames existed long before CFD and meshes. That clearly cannot be the definition! I think it goes all the way back to this guy named Euler.
But I guess it is now 2024 and we let codes can have whatever pronouns they want. |
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January 14, 2024, 04:23 |
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#7 | |
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Filippo Maria Denaro
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Quote:
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January 14, 2024, 07:54 |
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#8 |
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Do you mind sharing any references? I cannot find a single reference that states that Eulerian control volumes can move.
Kind regards
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January 14, 2024, 08:20 |
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#9 | |
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Filippo Maria Denaro
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Quote:
Forget for a moment the CFD and go to the fundamental fluid mechanics textbooks, you will read that a control volume moving at a prescribed arbitrary velocity is still an Eulerian framework. Only when the volume moves by means of the mapping of the flow velocity that is called Lagrangian. |
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January 14, 2024, 09:46 |
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#10 | |
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Quote:
If the equations are written in a absolute fixed frame, one can see that the analysis above cannot be used to model a true rotating object (as in my first post above) where the angle of the rectangle is changing over time (See this animation for illustration: https://www.youtube.com/watch?v=b0Gf8TRdWGo). My conclusion is that an Eulerian description for trully moving meshes in absolute frames does not make much sense. I appreciate any suggestions/corrections
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January 14, 2024, 10:09 |
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#11 |
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Lucky
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The approach you show in your own post is an example of a case where the mesh is attached to the reference frame. Even if you provided no picture, it would be implied anyway if you are use a sliding mesh. Because otherwise, there would be no reason to be using a sliding mesh.
Not all moving meshes are Eulerian but that was not your question. Still, even if you were modeling flow in aortic valves mounted on a rocket engine orbiting a star, that would still (most likely) be an Eulerian formulation as long as you are using simple definitions of derivatives. You can have arbitrary mesh motion and it remains Eulerian. It only becomes Lagrangian when you start using the material derivative. Lagrangian formulations exist in specialized codes but that is extremely far fetched from what your question is. It doesn't become Lagrangian just because it moves, Eulerian grids can move anywhere they like. So, answered already. There is no general special name for what you show in your picture because it's not special. |
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January 14, 2024, 15:19 |
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#12 |
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Joern Beilke
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January 15, 2024, 04:25 |
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#13 | ||
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Quote:
Quote:
Reference: [1] DONEA, Jean, HUERTA, Antonio, PONTHOT, J.‐Ph, et al. Arbitrary Lagrangian–Eulerian Methods. Encyclopedia of computational mechanics, 2004.
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January 15, 2024, 04:56 |
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#14 | |
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Filippo Maria Denaro
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Quote:
In my opinion, a Lagrangian grid is defined only when it moves according to the flow. Any other type of arbitrary moving mesh remains Eulerian. |
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January 15, 2024, 08:36 |
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#15 |
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Lucky
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The whole point of ALE is to use mesh coordinates, allowing a purely Eulerian framework to solve the problem of moving boundaries.
Every unstructured FVM solver I've ever seen uses mesh coordinates since you must always compute the face fluxes based on adjacent neighbor pairs. This would make the vast majority of FVM (and CFD) codes ALE codes. Even if I assume that the politically correct name for such a formulation is ALE and not almost purely Eulerian (APE), that would make virtually all CFD codes ALE and not APEs. Again, not special. ALE's are the CFD version of the Apache Helicopter meme. |
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