Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
From MaRDI portal
Publication:1092649
DOI10.1016/0021-9991(87)90170-7zbMath0627.65146OpenAlexW4232904039MaRDI QIDQ1092649
Warren F. jun. Miller, Edward W. Larsen, Jim E. Morel
Publication date: 1987
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-9991(87)90170-7
asymptotic expansionradiative transfermesh sizeneutron transportdiffusion theoryspatial differencing schemesNumerical examplesdiscrete-ordinates transport equations
Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Transport processes in time-dependent statistical mechanics (82C70) Radiative transfer in astronomy and astrophysics (85A25)
Related Items
Accelerated Simulation of Boltzmann-BGK Equations near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo ⋮ Discrete unified gas kinetic scheme for steady multiscale neutron transport ⋮ An asymptotic preserving unified gas kinetic particle method for radiative transfer equations ⋮ Asymptotic-preserving schemes for multiscale physical problems ⋮ Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer ⋮ A variable Eddington factor method with different spatial discretizations for the radiative transfer equation and the hydrodynamics/radiation-moment equations ⋮ Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation ⋮ A numerical method for nonstationary transport equations in diffusive regimes ⋮ A positive and asymptotic preserving filtered \(P_N\) method for the gray radiative transfer equations ⋮ Newton's method for optimal temperature-tracking of glass cooling processes ⋮ A spatial-temporal asymptotic preserving scheme for radiation magnetohydrodynamics in the equilibrium and non-equilibrium diffusion limit ⋮ An asymptotic preserving method for the linear transport equation on general meshes ⋮ NUMERICAL PASSAGE FROM RADIATIVE HEAT TRANSFER TO NONLINEAR DIFFUSION MODELS ⋮ An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations ⋮ Improved Mixed and Hybrid Discretization of the Transport Equation in Slab Geometry ⋮ Diffusion Limit of a Small Mean Free Path of Radiative Transfer Equations with Absorbing Boundary Condition ⋮ Diffusion Limit of Small Mean Free Path of Transfer Equation in ⋮ A hybrid Godunov method for radiation hydrodynamics ⋮ A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources ⋮ A weakly penalized discontinuous Galerkin method for radiation in dense, scattering media ⋮ An asymptotic-preserving IMEX method for nonlinear radiative transfer equation ⋮ Cellwise Block Iteration as a Multigrid Smoother for Discrete-Ordinates Radiation-Transport Calculations ⋮ Variable Eddington Factor Method for the SN Equations with Lumped Discontinuous Galerkin Spatial Discretization Coupled to a Drift-Diffusion Acceleration Equation with Mixed Finite-Element Discretization ⋮ A Least-Squares Transport Equation Compatible with Voids ⋮ The Asymptotic Drift-Diffusion Limit of Thermal Neutrons ⋮ Implicit Monte Carlo with a Linear Discontinuous Finite Element Material Solution and Piecewise Non-Constant Opacity ⋮ On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models ⋮ An asymptotic-preserving semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation ⋮ The discrete-ordinate method in diffusive regimes ⋮ A modified linear discontinuous spatial discretization method in planar geometry ⋮ Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving method ⋮ An asymptotic-preserving all-speed scheme for the Euler and Navier-Stokes equations ⋮ High order asymptotic preserving discontinuous Galerkin methods for gray radiative transfer equations ⋮ Study of Shock Structures Using the Unified Gas-Kinetic Wave-Particle Method with Various BGK Models ⋮ UGKS-Based Implicit Iterative Method for Multiscale Nonequilibrium Flow Simulations ⋮ High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state \(S_N\) transport equations ⋮ A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh ⋮ An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings ⋮ An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations ⋮ Asymptotic-preserving methods and multiscale models for plasma physics ⋮ Uniform convergent scheme for discrete-ordinate radiative transport equation with discontinuous coefficients on unstructured quadrilateral meshes ⋮ Numerical solution of the time-dependent transport equation with pulsed sources ⋮ Adaptive positive nodal method for transport equation ⋮ An efficient asymptotic preserving Monte Carlo method for radiative transfer equations ⋮ Machine Learning Moment Closure Models for the Radiative Transfer Equation II: Enforcing Global Hyperbolicity in Gradient-Based Closures ⋮ Second-order discretization in space and time for radiation-hydrodynamics ⋮ Spatial second-order positive and asymptotic preserving unified gas kinetic schemes for radiative transfer equations ⋮ On Solution Regularity of the Two-Dimensional Radiation Transfer Equation and Its Implication on Numerical Convergence ⋮ A robust \(S_{N}\)-DG-approximation for radiation transport in optically thick and diffusive regimes ⋮ Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in implicit Monte Carlo ⋮ An Asymptotic Preserving Method for Transport Equations with Oscillatory Scattering Coefficients ⋮ Efficient Stochastic Asymptotic-Preserving Implicit-Explicit Methods for Transport Equations with Diffusive Scalings and Random Inputs ⋮ A cascadic multigrid asymptotic-preserving discrete ordinate discontinuous streamline diffusion method for radiative transfer equations with diffusive scalings ⋮ Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport ⋮ A non-negative moment-preserving spatial discretization scheme for the linearized Boltzmann transport equation in 1-D and 2-D Cartesian geometries ⋮ A multi-dimensional, moment-accelerated deterministic particle method for time-dependent, multi-frequency thermal radiative transfer problems ⋮ Asymptotic diffusion limit of the symbolic Monte-Carlo method for the transport equation. ⋮ A multigroup moment-accelerated deterministic particle solver for 1-D time-dependent thermal radiative transfer problems ⋮ A parallel unified gas kinetic scheme for three-dimensional multi-group neutron transport ⋮ An accurate, strictly-positive, nonlinear characteristic scheme for the discrete-ordinate equations ⋮ A variable Eddington factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing ⋮ Semi-implicit time integration for \(P_N\) thermal radiative transfer ⋮ Numerical analysis of time integration errors for nonequilibrium radiation diffusion ⋮ Fast Convergence and Asymptotic Preserving of the General Synthetic Iterative Scheme ⋮ The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation ⋮ A Hybrid Finite-Volume, Discontinuous Galerkin Discretization for the Radiative Transport Equation ⋮ Particle transport through scattering regions with clear layers and inclusions ⋮ An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits ⋮ A Uniformly Convergent Scheme for Radiative Transfer Equation in the Diffusion Limit Up to the Boundary and Interface Layers ⋮ Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation ⋮ The effects of slope limiting on asymptotic-preserving numerical methods for hyperbolic conservation laws ⋮ Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation ⋮ Asymptotic solution of light transport problems in optically thick luminescent media ⋮ Subcell balance methods for radiative transfer on arbitrary grids ⋮ Infinite-Medium Solutions of the Transport Equation, SNDiscretization Schemes, and the Diffusion Approximation ⋮ An Asymptotic Preserving Two-dimensional Staggered Grid Method for Multiscale Transport Equations ⋮ Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes ⋮ Implicit filtered \(P_N\) for high-energy density thermal radiation transport using discontinuous Galerkin finite elements ⋮ An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations ⋮ Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport ⋮ Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings ⋮ Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering ⋮ Multiscale radiative transfer in cylindrical coordinates ⋮ Numerical Methods for Multidimensional Radiative Transfer ⋮ A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem ⋮ Positive and Asymptotic Preserving Approximation of the Radiation Transport Equation ⋮ Neutrino transport in core collapse supernovae ⋮ Radiative Transfer in Two Adjoining Media: The Continuity of Thermal Flux and the Existence and Uniqueness of Solutions ⋮ A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving ⋮ Asymptotic analysis of the RS-IMEX scheme for the shallow water equations in one space dimension ⋮ A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations ⋮ Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations ⋮ Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. II ⋮ Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes ⋮ Analysis of an Asymptotic Preserving Scheme for Stochastic Linear Kinetic Equations in the Diffusion Limit ⋮ A Low-Rank Schwarz Method for Radiative Transfer Equation With Heterogeneous Scattering Coefficient ⋮ Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit ⋮ Asymptotic preserving numerical schemes for a non-classical radiation transport model for atmospheric clouds ⋮ A family of independent variable Eddington factor methods with efficient preconditioned iterative solvers ⋮ A reduced basis method for radiative transfer equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A New Fourth-Order Finite-Difference Method for Solving Discrete-Ordinates Slab Transport Equations
- Finite-Difference Approximations and Superconvergence for the Discrete-Ordinate Equations in Slab Geometry
- Group Velocity in Finite Difference Schemes
- Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation
- Asymptotic analysis of transport processes
- On the Spatial Differencing of the Discrete Ordinate Neutron Transport Equation