Accelerating the discrete ordinates method for the solution of the radiative transfer equation for planetary atmospheres.

Details Accelerating the discrete ordinates method for the solution of the radiative transfer equation for planetary atmospheres. Accelerating the discrete ordinates method for the solution of the radiative transfer equation for planetary atmospheres.

Oct 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jqsrt..56..609g&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 56, issue 4, pp. 609-616

Statistics

Computation

Radiative Transfer: Scattering, Radiative Transfer: Planetary Atmospheres

Scientific paper

The discrete ordinates method is widely used in one-dimensional radiative transfer problems. The equation of transfer contains an integral over all directions to represent the multiple scattering of radiation. In the discrete ordinates method one of the integrals can be performed after a Fourier expansion is made for the scattering function and the radiance. The remaining integral is replaced with a Gauss quadrature sum and a system of ordinary differential equations is found. The system of ODEs is linear, and can be solved together with the boundary conditions by standard matrix methods. It is well known that symmetry relationships allow the order of the matrices that occur in the eigenproblem to be reduced by a factor of two. However, the resulting gain in efficiency is strongly compromised by the size of the remaining tasks of calculating the particular solution, and determining the unknown coefficients from the boundary conditions. In this paper he author shows that further increases in computational efficiency are available. First he finds that the order of the matrix inversion that arises in the particular solution can be reduced. He then shows that the equations that determine the coefficients from the boundary conditions can be reduced in order in the case of a one-layer system with a nonLambertian reflecting surface.

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