{"title":"Diffusive limits of 2D well-balanced schemes\\\\for kinetic models of neutron transport","authors":"G. Bretti, L. Gosse, N. Vauchelet","doi":"10.1051/m2an/2021077","DOIUrl":null,"url":null,"abstract":"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. These findings are confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2021077","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
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. These findings are confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.
期刊介绍:
M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem.
Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.