A Fast and Stable Solution Method for the Radiative Transfer Problem

Radiative transfer theory considers radiation in turbid media and is used in a wide range of applications. This paper outlines a problem formulation and a solution method for the radiative transfer problem in multilayer scattering and absorbing media using discrete ordinate model geometry. A selection of different steps is brought together. The main contribution here is the synthesis of these steps, all of which have been used in different areas, but never all together in one method. First, all necessary steps to get a numerically stable solution procedure are treated, and then methods are introduced to increase the speed by a factor of several thousand. This includes methods for handling strongly forward-scattering media. The method is shown to be unconditionally stable, though the problem was previously considered numerically intractable.

[1]  W. Magnus,et al.  Formulas and theorems for the functions of mathematical physics , 1949 .

[2]  G. C. Wick.  über ebene Diffusionsprobleme , 1943 .

[3]  A. Schuster.  Radiation through a foggy atmosphere , 1903 .

[4]  G. Mie.  Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen , 1908 .

[5]  John William Strutt,et al.  XV. On the light from the sky, its polarization and colour , 1871 .

[6]  P. S Mudgett,et al.  Multiple scattering calculations for technology II , 1972 .

[7]  P. Kubelka,et al.  New contributions to the optics of intensely light-scattering materials. , 1954, Journal of the Optical Society of America.

[8]  Subrahmanyan Chandrasekhar,et al.  On the radiative equilibrium of a stellar atmosphere , 1944 .

[9]  P. Kubelka.  Ein Beitrag zur Optik der Farban striche , 1931 .

[10]  Robert Bruce Lindsay,et al.  On the Light from the Sky, its Polarization and Colour (1871) , 1970 .

[11]  Edward W. Larsen,et al.  A spectral nodal method for one-group X,Y-geometry discrete ordinates problems , 1992 .

[12]  A. Badruzzaman.  Nodal methods in transport theory , 1990 .

[13]  Knut Stamnes,et al.  A new multi-layer discrete ordinate approach to radiative transfer in vertically inhomogeneous atmospheres , 1984 .

[14]  Knut Stamnes,et al.  On the computation of angular distributions of radiation in planetary atmospheres , 1982 .

[15]  Knut Stamnes,et al.  A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres , 1981 .

[16]  W. Wiscombe.  The Delta–M Method: Rapid Yet Accurate Radiative Flux Calculations for Strongly Asymmetric Phase Functions , 1977 .

[17]  Edward W. Larsen,et al.  A numerical method for one-group slab-geometry discrete ordinates problems with no spatial truncation error , 1990 .

[18]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[19]  Subrahmanyan Chandrasekhar,et al.  On the Radiative Equilibrium of a Stellar Atmosphere. II. , 1944 .

[20]  Fernando Carvalho da Silva,et al.  Recent advances in spectral nodal methods for X,Y - geometry discrete ordinates deep penetration and eigenvalue problems , 1999 .

[21]  L. Richards,et al.  Multiple scattering calculations for technology. , 1971, Applied optics.

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .

[23]  J. Sykes,et al.  Approximate integration of the equation of transger , 1951 .

[24]  Jim E. Morel,et al.  A Hybrid Collocation-Galerkin-Sn Method for Solving the Boltzmann Transport Equation , 1989 .

[25]  Gene H. Golub,et al.  Calculation of Gauss quadrature rules , 1967, Milestones in Matrix Computation.

[26]  L. C. Henyey,et al.  Diffuse radiation in the Galaxy , 1940 .

[27]  G. Rybicki.  Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.

[28]  Teruyuki Nakajima,et al.  Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation , 1988 .

[29]  Michael D. King,et al.  Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres. , 1983 .

[30]  Knut Stamnes,et al.  Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system. , 1994, Applied optics.

[31]  P. Kubelka,et al.  New Contributions to the Optics of Intensely Light-Scattering Materials. Part I , 1948 .