Improvements of the Environment Radiation Fields Modeling Numerical Methods on the Basis of Mirror Symmetry Principle

O. I. Smoktiy

St. Petersburg Institute for Informatics and Automation of RAS

Abstract: Fundamental properties of the angular-spatial symmetry of radiation fields in the uniform slab of a finite optical thickness are used for improvement of the numerical methods and algorithms of the classical radiative transfer theory. A new notion of so called photometrical invariants is introduced. The basic boundary-value problem of the radiative transfer theory is reformulated in new terms for the subsequent simplification of algorithms of numerical modeling methods such as spherical harmonics, discrete ordinates, Gauss-Seidel, Case and Hunt-Grant methods. This simplification leads to two-fold decrease of the ranks of linear algebraic equations with simultaneous reduction of numerical modeling intervals connected with angular and spatial variables.

Keywords: Mirror Reflection Principle, Photometrical Invariants, Boundary-Value Problem, Numerical Algorithms, Rank of Linear Equations System, Iteration, Spherical Harmonics, Discrete Ordinates, Gauss-Seidel, Case and Hunt-Grant Methods.

UDC: 551:523.3:535.35