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.
Keywords: Kinetic model of neutron transport, two-dimensional well-balanced, asymptotic-preserving scheme, Bessel functions, Laplace transforms, Pizzetti’s formula
@article{M2AN_2021__55_6_2949_0,
author = {Bretti, Gabriella and Gosse, Laurent and Vauchelet, Nicolas},
title = {Diffusive limits of {2D} well-balanced schemes for kinetic models of neutron transport},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2949--2980},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/m2an/2021077},
mrnumber = {4347301},
zbl = {1486.65096},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021077/}
}
TY - JOUR AU - Bretti, Gabriella AU - Gosse, Laurent AU - Vauchelet, Nicolas TI - Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2949 EP - 2980 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021077/ DO - 10.1051/m2an/2021077 LA - en ID - M2AN_2021__55_6_2949_0 ER -
%0 Journal Article %A Bretti, Gabriella %A Gosse, Laurent %A Vauchelet, Nicolas %T Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2949-2980 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021077/ %R 10.1051/m2an/2021077 %G en %F M2AN_2021__55_6_2949_0
Bretti, Gabriella; Gosse, Laurent; Vauchelet, Nicolas. Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2949-2980. doi: 10.1051/m2an/2021077
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