TY - JOUR

T1 - A new method of numerical solution of nonsteady problems in the theory of radiative transfer

AU - Grachev, S. I.

N1 - Funding Information: I wish to thank A. B. Schneeweiss for providing the program for calculating the redistribution function RII(x, x′). This work was supported by the “Leading Science Schools” grant No. 00-15-96607 from the Russian Fund for Fundamental Research, by the Astronomy federal program, and by the Integration program. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2001

Y1 - 2001

N2 - A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity oft, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + Δt, and so forth. The method enables one to analyze nonsteady (radiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples.

AB - A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity oft, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + Δt, and so forth. The method enables one to analyze nonsteady (radiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples.

UR - http://www.scopus.com/inward/record.url?scp=52549114467&partnerID=8YFLogxK

U2 - 10.1023/A:1014257123591

DO - 10.1023/A:1014257123591

M3 - Article

AN - SCOPUS:52549114467

VL - 44

SP - 505

EP - 517

JO - Astrophysics

JF - Astrophysics

SN - 0571-7256

IS - 4

ER -