Accession Number : AD0652089

Title :   A NUMERICAL METHOD FOR SOLVING THE EQUATION OF TRANSFER.

Descriptive Note : Technical information series,

Corporate Author : GENERAL ELECTRIC CO PHILADELPHIA PA MISSILE AND SPACE DIV

Personal Author(s) : Gray,E. L.

Report Date : MAY 1967

Pagination or Media Count : 74

Abstract : A method is presented for numerically computing solutions to the equation of radiative transfer for plane parallel atmospheres. As part of the computational scheme, the intensity distribution is computed within the atmosphere, thus providing vertical, directionally dependent, intensity profiles as well as the intensity of radiation emerging from either boundary of the atmosphere. Since the present effort is one mainly of testing the feasibility of the scheme, the case of conservative molecular scattering was chosen, so that the results could be compared with existing tabulations. Agreement is good for optically thin atmospheres, the error increasing as the optical thickness increases. This is attributable to the fact that: (1) Polarization effects are neglected in the present scheme. (2) Accuracy is diminished due to larger altitude increments for the larger optical thicknesses. The comparisons of the computations with the exact solutions are given, as well as some results of in-atmosphere intensity calculations. Convergence seems assured for total normal optical thicknesses < or = .50. Judgment for thicker atmospheres must await an expanded program which allows for more vertical subdivisions. In conclusion, the method seems feasible, and the hope is that modifications of the method may be used for more general laws of scattering, inclusion of absorption effects, and so forth.

Descriptors :   (*RAYLEIGH SCATTERING, *POLARIZATION), (*NUMERICAL METHODS AND PROCEDURES, *PROBLEM SOLVING), DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, FEASIBILITY STUDIES, INTENSITY, TABLES(DATA), OPTICS, THICKNESS, ACCURACY, CONVERGENCE, ERRORS, ATMOSPHERES, EARTH(PLANET), FUNCTIONS(MATHEMATICS)

Subject Categories : Numerical Mathematics
      Optics

Distribution Statement : APPROVED FOR PUBLIC RELEASE