Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE(2021)
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.
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关键词
Kinetic model of neutron transport, two-dimensional well-balanced, asymptotic-preserving scheme, Bessel functions, Laplace transforms, Pizzetti's formula
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