MOOSE workflow for strongly coupled（Single matrix）and eigenvalue formulations in MOOSE

[Jiang-JL111]

Check these boxes if you have followed the posting rules.

• Q&A General is the most appropriate section for my question
• I have consulted the posting Guidelines on the Discussions front page
• I have searched the Discussions forum and my question has not been asked before
• I have searched the MOOSE website and the documentation does not answer my question
• I have formatted my post following the posting guidelines (screenshots as a last resort, triple back quotes around pasted text)

Question

I am trying to implement a fully coupled neutronics–thermal-hydraulics (TH) model in MOOSE.
Specifically, I would like both physics (neutronics and TH) to be solved within a single nonlinear system and a single Jacobian, rather than using traditional iterative or MultiApp-based coupling.
I would like to ask several questions regarding the recommended solver strategy and the feasibility of fully coupled formulations in MOOSE:
1.What is the recommended Executioner for achieving a fully monolithic (simultaneous) neutronics–TH solve?I want to use the JFNK method to obtain a fully coupled steady-state solution of the multiphysics system, where the neutronics field is solved in its eigenvalue steady state and the thermal–hydraulics field is solved in its nonlinear steady state simultaneously.
2.Is it possible to run an eigenvalue calculation (Eigenvalue Executioner) when the neutronics equations are coupled monolithically with TH equations?My understanding is that adding TH PDEs breaks the standard linear homogeneous eigenvalue structure.
3.Overall, what is the recommended MOOSE workflow for strongly coupled (monolithic) multi-physics that involves neutronics + thermal-hydraulics?
Any guidance on solver selection, executioner configuration, or model architecture would be greatly appreciated！
Thank you very much!

[lindsayad]

I don't really think it makes mathematical sense to only perform an eigen calculation for a subset of an operator. In Introduction to Moltres we illustrated transient calculations marching to steady-state in which multigroup diffusion neutronics was coupled with fluid and solid heat transfer equations in a single monolithic matrix for simulating the MSRE. In that paper we assumed a constant velocity in the coolant but you could also incorporate the full Navier-Stokes equations if you wished. Perhaps @smpark7 could comment on whether that work has been extended since then

[smpark7]

I've used the monolithic approach in my earlier work, but I prefer to use iterative coupling now. The monolithic approach faces convergence and memory issues once you get into larger problem sizes unless you tailor a very effective preconditioner for it (this is non-trivial). I found myself stuck with using ASM-LU due to the advection terms in TH. Hypre-BoomerAMG is way more performant and memory-efficient for the neutron diffusion equations. I suppose you could apply a field split preconditioner, but I have no experience with that. Given other considerations, such as different mesh requirements, time scales, etc., I recommend iterative coupling as I've answered previously.

If @Jiang-JL111 insists on doing monolithic solves with neutronics eigen calculation (and perhaps it'll work for you because your model is small enough, e.g., coarse-mesh 2-D RZ), I have been able to run a neutron diffusion eigen calculation and steady-state heat conduction with the Eigenvalue executioner and a scaled heat source kernel for fixed power output. But this is with hypre-boomeramg, which usually does not work once you add advection terms.

[lindsayad]

Thanks for the answer @smpark7. I didn't know about the previous Moltres discussion post.

If @Jiang-JL111 wants to pursue field split preconditioning, I can help with that