Issue |
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
|
|
---|---|---|
Page(s) | 2949 - 2980 | |
DOI | https://doi.org/10.1051/m2an/2021077 | |
Published online | 06 December 2021 |
Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport
1
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: l.gosse@ba.iac.cnr.it
Received:
4
March
2020
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.
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