Improvements of the Environment Radiation Fields Modeling Numerical Methods on the Basis of Mirror Symmetry Principle
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 MethodsAbstract
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.Published
2014-06-30
How to Cite
Smokty, O. (2014). Improvements of the Environment Radiation Fields Modeling Numerical Methods on the Basis of Mirror Symmetry Principle. SPIIRAS Proceedings, 3(34), 57-88. https://doi.org/10.15622/sp.34.4
Section
Articles
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