Time Dependent Radiative Transfer Problems in a One-Dimensional Medium

Astrophysics ◽  
2021 ◽  
Author(s):  
A. G. Nikoghossian
Keyword(s):  
Radiative Transfer ◽  
Time Dependent ◽  
One Dimensional ◽  
Transfer Problems

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1

2002 ◽  
Vol 124 (4) ◽  
pp. 674-684 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Differential Equations ◽  
Order Approximation ◽  
High Order ◽  
High Order Approximation ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Transfer Problems

A high order approximation, the SKN method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The SKN solutions are compared with the exact, PN, and SN solutions. The SK1 and SK2 approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

The Solution of Transient Radiative Transfer With Collimated Incident Serial Pulse in a Plane-Parallel Medium by the DRESOR Method

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Qiang Cheng ◽  
Huai-Chun Zhou ◽  
Zhi-Feng Huang ◽  
Yong-Lin Yu ◽  
De-Xiu Huang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Transfer ◽  
Incident Radiation ◽  
Anisotropic Scattering ◽  
Time Dependent ◽  
Temporal Response ◽  
One Dimensional ◽  
Unit Energy ◽  
The Monte Carlo Method

A time-dependent distribution of ratios of energy scattered by the medium or reflected by the boundary surfaces (DRESOR) method was proposed to solve the transient radiative transfer in a one-dimensional slab. This slab is filled with an absorbing, scattering, and nonemitting medium and exposed to a collimated, incident serial pulse with different pulse shapes and pulse widths. The time-dependent DRESOR values, representing the temporal response of an instantaneous, incident pulse with unit energy and the same incident direction as that for the serial pulse, were proposed and calculated by the Monte Carlo method. The temporal radiative intensity inside the medium with high directional resolution can be obtained from the time-dependent DRESOR values. The transient incident radiation results obtained by the DRESOR method were compared to those obtained with the Monte Carlo method, and good agreements were achieved. Influences of the pulse shape and width, reflectivity of the boundary, scattering albedo, optical thickness, and anisotropic scattering on the transient radiative transfer, especially the temporal response along different directions, were investigated.

Discrete space theory of radiative transfer II. Stability and non-negativity

1969 ◽  
Vol 313 (1513) ◽  
pp. 199-216 ◽  
Keyword(s):  
Radiative Transfer ◽  
Discrete Space ◽  
Space Theory ◽  
One Dimensional ◽  
Mathematical Proofs ◽  
The Stability ◽  
Transfer Problems

A number of algorithms for solving one-dimensional monochromatic radiative transfer problems were summarized in Grant & Hunt (1968 b ). This paper is concerned with the mathematical proofs of existence and non-negativity of the solutions, together with the stability of the algorithms. These results may be obtained with very general assumptions, and permit us to use the algorithms in practical problems with confidence. Numerical evi­dence is presented to support the main conclusions.

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