A Nonlinear Hyperbolic Model for Radiative Transfer Equation in Slab Geometry

DOI10.1137/19M126774XzbMath1455.35247arXiv1911.05472OpenAlexW3098675970MaRDI QIDQ5139098

Lingchao Zheng, Ruo Li, Yu-Wei Fan

Publication date: 7 December 2020

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.05472

zbMATH Keywords

nonlinear modelradiative transfer equationslab geometryglobal hyperbolicitygeneralized Rankine-Hugoniot conditionnonconservative systemtwo-beam problemanti-diffusive radiation flowGaussian source problemgeneralized hyperbolic regularizationSu-Olson problem

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Transport processes in time-dependent statistical mechanics (82C70) Initial value problems for first-order hyperbolic systems (35L45) Waves and radiation in optics and electromagnetic theory (78A40) First-order hyperbolic systems (35L40) Physical optics (78A10) Method of moments applied to problems in optics and electromagnetic theory (78M05) First-order hyperbolic equations (35L02) Spectral, collocation and related methods applied to problems in optics and electromagnetic theory (78M22)

Related Items (10)

Machine learning moment closure models for the radiative transfer equation. I: Directly learning a gradient based closure ⋮ Hyperbolic Quadrature Method of Moments for the One-Dimensional Kinetic Equation ⋮ Machine learning moment closure models for the radiative transfer equation. III: enforcing hyperbolicity and physical characteristic speeds ⋮ Machine Learning Moment Closure Models for the Radiative Transfer Equation II: Enforcing Global Hyperbolicity in Gradient-Based Closures ⋮ Some recent advances on the method of moments in kinetic theory ⋮ Nonrelativistic limit of the Euler‐HMP_N approximation models arising in radiation hydrodynamics ⋮ A hybrid moment method for multi-scale kinetic equations based on maximum entropy principle ⋮ Navier-Stokes limit of globally hyperbolic moment equations ⋮ Direct Flux Gradient Approximation to Moment Closure of Kinetic Equations ⋮ A Nonlinear Moment Model for Radiative Transfer Equation

Uses Software

• OPQ

Cites Work

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