Study and evaluation of the Ronen Method accuracy at material interfaces

TL;DR

This paper evaluates the Ronen Method's accuracy at material interfaces, demonstrating significant improvements in flux distribution precision through iterative refinement and boundary approximation adjustments.

Contribution

It verifies the equivalence of diffusion and transport solutions with optimal diffusion coefficients and assesses the Ronen Method's enhanced accuracy near interfaces and boundaries.

Findings

Ronen Method achieves flux deviations around 0.01% at interfaces.

Iterative refinement greatly improves flux accuracy.

Method is robust across different boundary approximations.

Abstract

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.