  The Ronen method (RM) demands for successive resolutions of the diffusion
equation where local diffusion constants are modified to reproduce more
accurate estimates of the currents by a transport operator. The methodology is
currently formulated by using the formalism of the collision probability method
(CPM) for the current evaluation and RM was recently tested on a complete suite
of one-dimensional multigroup benchmark problems. Small differences in the flux
(less than 2%) were reported at material interfaces and close to the vacuum
boundary with respect to the reference solution from transport (CPM). In this
work, a verification check is first set to prove an equivalence between
diffusion and transport when optimal diffusion coefficients are computed by the
transport solution itself and employed in a standard diffusion calculation. 1G
and 2G criticality problems from the same criticality benchmark test suite of
previous publications are tested. Then, the accuracy of the flux distribution
near the vacuum boundary and material interfaces is computed using the RM for
different approximations of the vacuum boundary and with respect to decreasing
values of the RM convergence criterion set in its iterative scheme. Indeed, the
RM calculates more accurate flux distribution at all material interfaces,
regardless of the initial values used for the diffusion coefficient and the
extrapolated distance at the beginning of the iterative process. Maximal flux
deviations fall everywhere around 0.01% when the RM convergence criterion is
set to ten significant digits, leading to two orders of magnitude improvement
in the flux deviation.
