Hybrid deterministic/Monte Carlo neutronics (Q2870668)

The authors propose a hybrid deterministic/Monte Carlo solver for the monoenergetic transport equation in slab geometry with isotropic scattering NEWLINE\[NEWLINE \mu\frac{\partial\psi(x,\mu)}{\partial x} +\Sigma_t(x)\psi(x,\mu) =\frac{1}{2}[\Sigma_s(x)\int_{-1}^{1}\psi(x,\mu')d\mu'+q(x)]NEWLINE\]NEWLINE for \(0<x<\tau\) and \( \mu\in[-1,0)\cup(0,1]\) and boundary conditions NEWLINE\[NEWLINE \psi(0,\psi)=\psi_l(\mu),\, \mu>0;\,\psi(\tau,\mu)=\psi_{\tau},\, \mu<0.NEWLINE\]NEWLINE The authors derive a new analytic formula for the Jacobian-vector product within the Jacobian-free Newton-Krylov algorithm. The motivation for this is to alleviate the Monte Carlo noise issues which will be amplified within the standard finite-difference Jacobian-vector product approximation. The impact on algorithm performance driven by different choices for Monte Carlo tally procedures is also considered.