This is my first topic and first of all i would like to thank all the developing community of OpenMC for the great contribution you are doing to science and nuclear engineering. For being an open source code, i strongly believe that in a few years OpenMC will be the most relevant Monte Carlo transport code in the world.
My question concerns the Functional Expansion Filters. In the documentation, it is stated that the following integral is estimated stochastically (in the case of Legendre Polynomials):
How exactly it is done? I don’t understand how you can estimate this integral if a continuous function for the flux is not known a priori. Besides, what this flux as a function of the z coordinate represents in a 3D problem? Is it the mean value of the flux over all x and y coordinates? In what units is the flux given when you expand it as a Legendre Polynomial?
@Artur thank you for your kind words! Regarding your question, it is correct that the continuous flux is not known a priori. A Monte Carlo simulation generally can’t give you the continuous flux at specific points, but it is very good at calculating integrals of the flux (possibly multiplied by some function) over a spatial domain. I would suggest reading our theory guide on tallies if this is not clear. In the case of FETs, we calculate the volume-integral of the flux multiplied by Legendre polynomials (this is what the code is tallying during the simulation), which happens to be an estimate of the expansion coefficients needed. Thus, after the simulation, we can reconstruct an estimate of the continuous spatial variation of the flux through the functional expansion.
@paulromano thank you for the reply. I think i get it know. The flux is integrated over thin layers perpendicular to the z coordinate (or any other specified coordinate) and is multiplied by the Legendre Polynomial evaluated at the middle point (or any other point) of the layer. Then, the value for all layers are summed up and this is an estimate for the integral above. Is that correct?
Not quite. There are no layers at all. The tally is performed over the entire length that is being approximated by the functional expansion. The tally scores give you spatial Legendre moments of the flux, which, as discussed above, are the coefficients that are needed for an expansion.
