How to implement CMFD on continuous FEM

[hityyds]

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Question

Hi, everyone.

I want to implement CMFD (Coarse Mesh Finite Difference method) on CFEM (Continuous Finite Element Method), i.e. the transport calculations are based on the CFEM method. However, there are shared Nodes between different elements of the CFEM mesh, so when accelerating the transport fluxes based on the results of the coarse mesh, there is a question of which Elem the Node should be based on to do the scaling of its fluxes? For example, a Node may be shared by four Elems, and their scaling ratios are 1, 2, 3, and 4 respectively, how should the flux scaling ratio of this Node be determined?

Thank you for your attention. Hopefully someone can give advice.

[GiudGiud]

Hello

I would suggest to blend the 4 ratios together.
At convergence, all scaling ratios will be 1 so it wont matter.

Guillaume

[hityyds]

Thank you for your response. I tried using the average ratio, but it still didn't work. I tested it, and the program runs correctly if I add the DGKernel, but it fails when I remove it. I think this might be because using the average ratio disrupts the local consistency between the coarse and fine meshes. After this processing, the flux at this node doesn't reach its ideal value for all four elements.

[hityyds]

From this perspective, CFEM and CMFD are incompatible. I'm ready to give up. Thank you again for your advice.

[lindsayad]

@YaqiWang @jthano do you guys do CMFD with CFEM?

[hityyds]

Thank you for your attention, but I'm ready to give up. I have tried using the average ratio, but it still didn't work. I tested it, and the program runs correctly if I add the DGKernel, but it fails when I remove it. I think this might be because using the average ratio disrupts the local consistency between the coarse and fine meshes. After this processing, the flux at this node doesn't reach its ideal value for all four elements. From this perspective, CFEM and CMFD are incompatible.

[YaqiWang]

No. It is possible (https://www.tandfonline.com/doi/abs/10.13182/NSE12-50). We typically do fine mesh diffusion acceleration with CFEM (https://www.tandfonline.com/doi/abs/10.13182/NSE12-83). We do CMFD typically with DFEM (https://doi.org/10.1016/j.anucene.2024.110365).

[hityyds]

Thank you for the reminder. I will carefully study the content of these articles.