Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering

References

• Aronson, R. 1984. Subcritical problems in spherical geometry. Nucl. Sci. Eng. 86 (2): 136–49. doi:10.13182/NSE86-136
   Web of Science ®Google Scholar
• Carlson, B. G., and K. D. Lathrop. 1968. Transport theory – the method of discrete ordinates. Computing Methods in Reactor Physics, ed. H. Greenspan, C. N. Keller and D. Okrent, 197. New York: Gordon and Breach.
   Google Scholar
• Case, K. M. 1960. Elementary solutions of the transport equation and their properties. Ann. Phys. 9 (1): 1–23. doi:10.1016/0003-4916(60)90060-9
   Web of Science ®Google Scholar
• Case, K. M., and P. F. Zweifel. 1967. Linear Transport Theory. Reading, Massachusetts: Addison-Wesley Publishing Company. section 4.5, 70. Eq. (19).
   Google Scholar
• Dahl, B. 1985. Numerical solutions of the monoenergetic neutron transport equation with anisotropic scattering, Report CTH-RF-49, 7. Eq. (2.21) - Chalmers University of Technology, Gothenburg, Sweden.
   Google Scholar
• Davison, B., and J. B. Sykes. 1958. Neutron Transport Theory, 235. Oxford: Calrendon Press. Eq. (17.15).
   Google Scholar
• Erdelyi, A., W. Magnus, F. Oberhettinger, and F. G. Tricomi. 1954. Tables of integral transforms, vol 1, 249. New York, Toronto, London: McGraw Hill Book Company, Inc. section 5.6 (35).
   Google Scholar
• Ganapol, B. cited as Private Communications by A. Yilmazer and C. Kocar ibid.
   Google Scholar
• Garcia, R. D. M., C. E. Siewert, and J. R. Thomas. 2017. Thomas - a computationally viable version of the PN method for spheres. Nucl. Sci. Eng. 186 (2): 103–19. doi:10.1080/00295639.2016.1273627
   Web of Science ®Google Scholar
• Gibbs, A. G. 1969. Analytical solutions of the neutron transport equation in arbitrary convex geometry. J. Math. Phys. 10 (5): 875–90. doi:10.1063/1.1664917
   Web of Science ®Google Scholar
• Kofink, W. 1958. New solutions of Boltzmann equation for monoenergetic neutron transport in spherical geometry. Oak Ridge National Laboratory Report ORNL 3216.
   Google Scholar
• Mika, J. R. 1961. Neutron transport with anisotropic scattering. Nucl. Sci. Eng. 11 (4): 415–27. doi:10.13182/NSE61-1
   Web of Science ®Google Scholar
• Mitsis, G. J. 1963. Transport Solutions to the Monoenergetic Critical Problems, Report ANL 6787, Argonne National Laboratory.
   Google Scholar
• Muskhelishvili, N. I. 1958. Singular integral equations. Groningen, Netherlands: Wolters-Noordhoff Publishing. Chapter 5, Section 85, 88.
   Google Scholar
• Sahni, D. C. 1966. The effect of black sphere on the flux distribution in an infinite moderator. J. Nucl. Energy, Parts A/B 20 (11–12): 915–20. doi:10.1016/0368-3230(66)90129-7
   Google Scholar
• Sahni, D. C. 1988. New diffusion-like solutions of one-speed transport equation in spherical geometry. Ann. Nucl. Energy 15 (7): 357–62. doi:10.1016/0306-4549(88)90083-7
   Web of Science ®Google Scholar
• Sahni, D. C., and A. Sharma. 2000. Computation of higher spherical harmonics moments of the angular flux for neutron transport problems in spherical geometry. Ann. Nucl. Energy 27 (5): 411–33. doi:10.1016/S0306-4549(99)00062-6
   Web of Science ®Google Scholar
• Sahni, D. C., and R. G. Tureci. 2018. Discrete Eigenvalues of case spectrum with anisotropic scattering. Nucl. Sci. Eng. 191 (2):121–35. doi:10.1080/00295639.2018.1463748
   Web of Science ®Google Scholar
• Sanchez, R. 1986. Integral form of the equation of transfer for a homogeneous sphere with linearly anisotropic scattering. Trans. Theory Stat. Phys 15 (3): 333–43. doi:10.1080/00411458608210456
   Google Scholar
• Siewert, C. E., and P. Grandjean. 1979. Three Basic Neutron Transport Problems in Spherical Geometry. Nucl. Sci. Eng 70 (1): 96–8. doi:10.13182/NSE70-96
   Web of Science ®Google Scholar
• Sjöstrand, N. G. 1988. One-speed neutron transport in spheres with totally absorbing cores. Transp. Theory Stat. Phys. 17 (4):443–59. doi:10.1080/00411458808230874
   Google Scholar
• Tureci, R. G., D. C. Sahni, A. Aydin, and A. Z. Bozkir. 2021. Half-Space Albedo Problem for Linear-Triplet Anisotropic Scattering, (under preparation).
   Google Scholar
• Vieira, W. J., A. D. Caldeira, and R. D. M. Garcia. 2019. A comparison of transport methods for the solution of a problem with shadowing effects in spherical geometry. Ann. Nucl. Energy 134:370–5. doi:10.1016/j.anucene.2019.06.012
   Web of Science ®Google Scholar
• Watson, G. N. 1922. A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press. Chapter XI, section 11.5, 369. Eq. (4).
   Google Scholar
• YilMazer, A., and C. Kocar. 2009. Some Benchmark Results in Spherical Media Radiative Transfer Problems. Transp. Theory Stat. Phys. 38 (5):273–92. doi:10.1080/00411450903238707
   Web of Science ®Google Scholar