Volume 55, Number 6, November-December 2021
|Page(s)||2949 - 2980|
|Published online||06 December 2021|
Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport
Istituto per le Applicazioni del Calcolo, via dei Taurini, 19 00185 Rome, Italy
2 Univ. Sorbonne Paris Nord, Labo. Analyse, Géométrie et Applications, CNRS UMR 7539, F-93430 Villetaneuse, France
* Corresponding author: firstname.lastname@example.org
Accepted: 17 November 2021
Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping, allowing to derive a scattering S-matrix and corresponding "truly 2D well-balanced" numerical schemes. A first scheme is obtained by directly implementing truncated Fourier–Bessel series, whereas another proceeds by applying an exponential modulation to a former, conservative, one. Consistency with the asymptotic damped parabolic approximation is checked for both algorithms. A striking property of some of these schemes is that they can be proved to be both 2D well-balanced and asymptotic-preserving in the parabolic limit, even when setting up IMEX time-integrators: see Corollaries 3.4 and A.1. These findings are further confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.
Mathematics Subject Classification: 65M06 / 35K57 / 82D75
Key words: Kinetic model of neutron transport / two-dimensional well-balanced / asymptotic-preserving scheme / Bessel functions / Laplace transforms / Pizzetti’s formula
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.