Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space

Details Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982jqsrt..28..271o&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 28, Oct. 1982, p. 271-288.

Physics

13

Cloud Physics, Radiative Transfer, Spherical Harmonics, Approximation, Cartesian Coordinates, Partial Differential Equations, Spherical Coordinates

Scientific paper

The basic radiative transfer equation in three-dimensional space is expressed in terms of three commonly used coordinate systems, namely, Cartesian, cylindrical and spherical coordinates. The concept of a transformation matrix is applied to the transformation processes between the Cartesian system and two other systems. The spherical harmonic method is then applied to decompose the radiative transfer equation into a set of coupled partial differential equations for all three systems in terms of partial differential operators. By truncating the number of partial differential equations into four along with further mathematical analysis, we obtain a modified Helmholtz equation. For each coordinate system, analytical solutions in terms of infinite series are obtained whenever the equation is solvable by the technique of separation of variables with proper boundary conditions. Numerical computations are carried out for one dimensional radiative transfer to illustrate the applicability of the technique developed in the present study.

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