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[Robert Caulk <question695542@xxxxxxxxxxxxxxxxxxxxx>]

Question #695542 on Yade changed:
https://answers.launchpad.net/yade/+question/695542

Robert Caulk proposed the following answer:
If you only seek the maximum time step for the conduction, you would
consider the finite difference scheme currently employed and identify
the thermal resistivity that destabilizes the scheme. You need to
consider both resistivities associated with particle-particle and
particle-pore. In your current case, the Reynolds number (Nusselt)
contributes to the total thermal resistivity between the particle-pore.
Obviously, these thermal resistivities are highlighted in our paper [1].

In other words, you need to set up a finite difference approximation for
a single reservoir (particle) connected to other particles and other
pores, which is highlighted in the paper [1]. The consideration of
stability is simple, you consider this reservoir at 0 temperature
initial state, and perturb it by delta T. You can then use the resulting
finite-difference formulation to identify the timestep that prevents the
next temperature step from oscillating below 0.

Of course, this is only considering the stability of the finite-
difference conduction scheme. In your current case, you are also
considering advective heat transfer, which is two-way coupled with the
conduction scheme. Further, you are simulating fluid fluxes so there is
a maximum timestep associated with that implicit scheme - much more
computationally intensive to compute directly, but we highlight a method
in the appendix of our other paper [2]. So things can become complicated
if you do not know which regime you are in, or if your problem crosses
regimes.


[1]https://www.sciencedirect.com/science/article/abs/pii/S0045782520304771
[2]https://www.sciencedirect.com/science/article/abs/pii/S0010465519303340?via%3Dihub

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