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Are the DyM solvers considered to be ALE methods?

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Old   February 27, 2018, 16:43
Default Are the DyM solvers considered to be ALE methods?
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Stephen Waite
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Hi everybody.

So I have seen a few papers around that state that solvers such as pimpleDyMFOAM are ALE methods, and indeed anything that seems to have deforming mesh nodes.

My understanding of mesh motion implemented in OpenFOAM for the dynamicFV classes was that it worked in the following way.

1) deform the mesh (move boundary nodes, handle interior mesh motion via chosen method such as Laplacian diffusion of FEM)
2) calculate the cell volume changes and the associated fluxes that occur from this change.
3) Solve current time step on the deformed mesh (so sensitive to cell quality on the now deformed mesh).

My understanding of ALE was;
1) Have two meshes that represent the fluid domain, one a material or spatial mesh that represents space and time, and undergoes similar deformations mentioned above, and a second, time independent Eulerian mesh that has a 1:1 cell mapping to the material mesh.
2) Map the volume fluxes from the material domain, to the Eulerian grid through some mapping function, and solve equations with nice cell quality.
3) Map results back to the material mesh, and perform next deformation step.

Am I incorrect about my understanding of how these methods work? Or are people just being a bit liberal with the term ALE, and applying it to any method that has movement of Eulerian mesh nodes?

Thanks for your time! I'm very confused.

Cheers
Stephen
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Old   January 23, 2019, 11:38
Default Answer: yes
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https://eprints.soton.ac.uk/166633/1/OF_Workshop.pdf
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Old   January 24, 2019, 11:51
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Santiago Lopez Castano
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Quote:
Originally Posted by Stephen Waite View Post
Hi everybody.

So I have seen a few papers around that state that solvers such as pimpleDyMFOAM are ALE methods, and indeed anything that seems to have deforming mesh nodes.

My understanding of mesh motion implemented in OpenFOAM for the dynamicFV classes was that it worked in the following way.

1) deform the mesh (move boundary nodes, handle interior mesh motion via chosen method such as Laplacian diffusion of FEM)
2) calculate the cell volume changes and the associated fluxes that occur from this change.
3) Solve current time step on the deformed mesh (so sensitive to cell quality on the now deformed mesh).

My understanding of ALE was;
1) Have two meshes that represent the fluid domain, one a material or spatial mesh that represents space and time, and undergoes similar deformations mentioned above, and a second, time independent Eulerian mesh that has a 1:1 cell mapping to the material mesh.
2) Map the volume fluxes from the material domain, to the Eulerian grid through some mapping function, and solve equations with nice cell quality.
3) Map results back to the material mesh, and perform next deformation step.

Am I incorrect about my understanding of how these methods work? Or are people just being a bit liberal with the term ALE, and applying it to any method that has movement of Eulerian mesh nodes?

Thanks for your time! I'm very confused.

Cheers
Stephen
The second description seems more like an holomorphic coordinate transformation, very commonly used in finite difference codes...
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