Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport

被引:0
|
作者
Bretti, Gabriella [1 ]
Gosse, Laurent [1 ]
Vauchelet, Nicolas [2 ]
机构
[1] Ist Applicaz Calcolo, Via Taurini 19, I-00185 Rome, Italy
[2] Univ Sorbonne Paris Nord, Labo Anal Geometrie & Applicat, CNRS UMR 7539, F-93430 Villetaneuse, France
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2021年 / 55卷 / 06期
关键词
Kinetic model of neutron transport; two-dimensional well-balanced; asymptotic-preserving scheme; Bessel functions; Laplace transforms; Pizzetti's formula; DECOMPOSITION; EQUATIONS;
D O I
10.1051/m2an/2021077
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:2949 / 2980
页数:32
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