On the PN Method in Spherical Geometry: A Stable Solution for the Exterior of a Sphere. Issue 4 (19th September 2018)

• Record Type: Journal Article
• Authors: Garcia, R. D. M.
• Is Part Of: Journal of computational and theoretical transport. Volume 47:Issue 4/6(2018)
• Page Start: 400
• Page End: 423
• Publication Date: 2018-09-19
• Subjects: Neutron transport -- spherical geometry -- PN method -- Volterra integral equations; Transport theory -- Periodicals; Statistical physics -- Periodicals; Statistical physics; Transport theory; Periodicals; 530.138
• DOI: 10.1080/23324309.2018.1489847
• Languages: English
• ISSNs: 2332-4309

Abstract

Abstract: A numerically stable version of the PN method for solving the one-speed problem of neutron transport in the exterior of a sphere is developed. A transformation is used to obtain a plane-geometry-like neutron transport equation, where the angular derivative part of the streaming term in spherical geometry is considered as a source. In this way, conventional PN solutions developed for plane geometry can be used to solve the problem and avoid having to deal with ill-conditioned solutions expressed in terms of the modified spherical Bessel functions of the third kind.