Time-Dependent Transport via the Continued Fraction Approximation.
Abstract
The time-dependent neutral particle transport problem of an isotropic Green's function source in homogeneous, isotropic, spherically symmetric media is examined using the infinite set of time-dependent P-N equations and integral transform techniques. The approximate Green's function solutions in transform space for the all-angle flux corresponding to the P-N approximation of order N are determined to order P-9, and demonstrate a multiple wave nature upon inversion. An examination of the set of P-N solutions leads to the development of the complete (P-infinity) continued fraction solution in transform space. For pure absorbing media the continued fraction is related to an analytic function which, upon inversion, yields the exact analytical solution to the problem. For cases with low-order scattering moments the continued fraction solution yields closed form functions in transform space, but these have not yielded to useful inversion. However, a continued fraction approximation technique is developed and yields simple closed form approximate solutions for the case of isotropic scatter. (Modified author abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1973
- Accession Number
- AD0766230
Entities
People
- Willaim A. Yingling
Organizations
- Air Force Research Laboratory