Why Can We Specify The Source Site Distribution

User Support
1

Hey Guys,

In the documentation, it says “Fortunately, regardless of the choice of initial source distribution, the method is guaranteed to converge to the true source distribution.”

If that’s the case, why are we allowed specify the initial source distribution with the tag in the first place? Shouldn’t it not matter what we pick?

I tried a little experiment where I modified the ‘reflective’ example’ to make a 2x2x2 infinite rectangular prism, and gave it ‘reflective’ boundary conditions all around. I then placed a point source at 0,0,0 and calculated k-eff. I then placed a point source at 0.5,0.5,0.5 and calculated k-eff.

I noticed a difference of about 1 milli-k in the calculations with 500 batches of 10K particles.

I then thought, ‘well, if my understanding is correct a better converged answer should give me k-eff values with a closer value’

So, I reran the experiment with 5000 batches at 10k particles each. Still about 1 milli-k difference.

so is my thinking correct in that I should get an answer which converges on a value regardless of where I place the initial source?

If that’s so, what would cause this difference in k-eff? What can I do to reduce it?

If that’s so, why does openMC allow us to specify the initial source distribution?

Thanks for any insight you guys might have.

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Hi Terry,

It is true that, in an eigenvalue problem, the choice of the initial source does not statistically affect the answer. If you remove the word ‘statistically’ you can also apply this statement to deterministic eigenvalue methods. The eigenvalue and eigenvector are a property of the multiplying system and not a function of the external source. What you are seeing is a validation of that fact (a small 1 milli-k reference), likely combined with too few inactive cycles so that the fission source distribution is not converged from your initial guesses.

This brings me to my next point: a choice is offered to the user for the initial source distribution because if the initial source distribution is exactly right, then theoretically no inactive cycles are needed, and the MC solver can just begin tallying results. This is how the coarse-mesh finite differencing (CMFD) acceleration method works - it essentially generates a diffusion-based problem (which preserves higher order physics by way of diffusion constant corrections based on the Monte Carlo tallied net neutron current at each coarse mesh surface), which propagates the source distribution more quickly than does the normal Monte Carlo transport process.

Finally, the solution to fixed source problems heavily depends on the source specified by the user, as you can imagine.

Hope this helps, let me know if you have any more questions,
Adam

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Hi Adam,

So, what I’ve heard you say is that my initial guess should only affect the number of cycles to convergence, but not the value of the convergence. If that’s the case, how can I make it so that my two cases converge to the same answer?

To be true, there are many things I don’t understand.

First, what are “higher order physics”, I’ve heard that phrase often, but I don’t understand what it means.I’m not sure what a ‘deterministic eigenvalue method’ is.
Why would changing the number of ‘inactive’ cycles change would my output?
I am not familiar with the CMFD acceleration method.

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The initial guess should affect the number of cycles to convergence, and if given infinite number of particles, not the value of convergence (of course you should expect some statistical noise in there). To make the two cases converge to the same answer, increase your inactive cycles count and increase your active particles (either active cycles or particles per batch) until they match within the error bars.

First, what are “higher order physics”, I’ve heard that phrase often, but I don’t understand what it means.

This is a term that, in reactor engineering, means models with less approximations. Transport theory methods (Monte Carlo as well as Sn, and MOC if you are familiar with these) is ‘higher order physics’ than is diffusion theory, as there are less approximations in them to the Boltzmann Transport Equation than in Diffusion Theory.

I’m not sure what a ‘deterministic eigenvalue method’ is.

A deterministic method is one where the transport equation is discretized (some combination of space, energy, angle discretizations) and a system of equations results; the highest eigenvalue of this system of equations is keff, and thus solving for the eigenvalue of these linear systems is akin to solving for keff.

Why would changing the number of ‘inactive’ cycles change would my output?

The role of inactive cycles in eigenvalue problems is to allow the Monte Carlo to ‘figure out’ the source particle distribution (space, energy and angle) of the system. If the inactive cycles were not enough, then the true source particle distribution will not have been found, and you will begin recording (tallying) results with an incorrect spatial, energy, angle distribution of source particles. This will change your answer.

I am not familiar with the CMFD acceleration method.

I’ll leave this to some papers on the internet (and linked to in the OpenMC documentation).

A good reference for alot of these areas is covered in the Los Alamos document LA-UR-05-4983.

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