Mixed singular-regular boundary conditions in multislab radiation transport

This article reports a computational method for approximately solving radiation transport problems with anisotropic scattering defined on multislab domains irradiated from one side with a beam of monoenergetic neutral particles. We assume here that the incident beam may have a monodirectional component and a continuously distributed component in angle. We begin by defining the target problem representing the class of radiation transport problems that we are focused on. We then Chandrasekhar decompose the target problem into an uncollided transport problem with left singular boundary conditions and a diffusive transport problem with regular boundary conditions. We perform an analysis of these problems to derive the exact solution of the uncollided transport problem and a discrete ordinates solution in open form to the diffusive transport problem. These solutions are the basis for the definition of a computational method for approximately solving the target problem. We illustrate the numerical accuracy of our method with three basic problems in radiative transfer and neutron transport, and we conclude this article with a discussion and directions for future work.

[1]  C. E. Siewert,et al.  A concise and accurate solution to Chandrasekhar’s basic problem in radiative transfer , 2000 .

[2]  Barry D Ganapol,et al.  LCM2: A coupled leaf/canopy radiative transfer model , 1999 .

[3]  B. L. Rushton,et al.  Epithermal Neutron Beam Design for Neutron Capture Therapy at the Power Burst Facility and the Brookhaven Medical Research Reactor , 1990 .

[4]  Marcos Pimenta de Abreu.  Numerical methods for the generation of the spectrum of the multigroup slab-geometry discrete ordinates operator in neutron transport theory , 2002 .

[5]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .

[6]  V. Klema.  LINPACK user's guide , 1980 .

[7]  J. Lenoble.  Radiative transfer in scattering and absorbing atmospheres: Standard computational procedures , 1985 .

[8]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[9]  C. Siewert,et al.  Benchmark results in radiative transfer , 1985 .

[10]  Edward W. Larsen,et al.  A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error , 1991 .

[11]  W. Verhoef.  Light scattering by leaf layers with application to canopy reflectance modelling: The SAIL model , 1984 .

[12]  C. Siewert,et al.  On multi-region problems in radiative transfer , 1979, Astrophysics and Space Science.

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

[14]  D. H. Card,et al.  Remote sensing of forest canopy and leaf biochemical contents , 1988 .

[15]  K. Stamnes,et al.  Radiative Transfer in the Atmosphere and Ocean , 1999 .

[16]  M. M. R. Williams,et al.  Mathematical methods in particle transport theory , 1971 .

[17]  R. Shefer,et al.  Accelerator-based epithermal neutron beam design for neutron capture therapy. , 1992, Medical physics.

[18]  W. W. Engle,et al.  A USERS MANUAL FOR ANISN: A ONE DIMENSIONAL DISCRETE ORDINATES TRANSPORT CODE WITH ANISOTROPIC SCATTERING. , 1967 .

[19]  Hermes Alves Filho,et al.  Progress in spectral nodal methods applied to discrete ordinates transport problems , 1998 .

[20]  Marcos Pimenta de Abreu,et al.  On the spectrum of the one-speed slab-geometry discrete ordinates operator in neutron transport theory , 1998 .

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

[22]  K. M. Heal,et al.  Maple V: Learning Guide , 1995 .

[23]  L. Johnson,et al.  LEAFMOD : A new within-leaf radiative transfer model , 1998 .

[24]  Samuel D. Conte,et al.  Elementary Numerical Analysis: An Algorithmic Approach , 1975 .

[25]  Hans Jan. Schneider,et al.  Matrices and Linear Algebra , 1973 .

[26]  Hermes Alves Filho,et al.  A numerical method for multigroup slab-geometry eigenvalue problems in transport theory with no spatial truncation error , 1996 .

[27]  Jeffery Lewins,et al.  Advances in Nuclear Science and Technology , 1983 .

[28]  Brian T. Smith,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[29]  M. Mesterton-Gibbons.  A Concrete Approach to Mathematical Modelling , 1989 .

[30]  Ranga B. Myneni,et al.  Photon-Vegetation Interactions , 1991, Springer Berlin Heidelberg.