2015/05/28 by Cory Ahrens, Cory D. Ahrens
Engineering · Mathematics · #Gas Dynamics and Kinetic Theory #Nuclear reactor physics and engineering #Radiative Heat Transfer Studies
paper · doi:10.13182/nse14-76
openalex publication_date 2015/05/28 · crossref created 2015/05/28 · crossref issued 2015/07/01 · crossref published 2015/07/01 · crossref published-print 2015/07/01 · crossref published-online 2017/03/22 · crossref deposited 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06 · crossref indexed 2026/08/03
The classical Sn equations of Carlson and Lee have been a mainstay in multidimensional radiation transport calculations. In this paper, an alternative to the Sn equations, the “Lagrange Discrete Ordinates” (LDO) equations, are derived. These equations are based on an interpolatory framework for functions on the unit sphere in three dimensions. While the LDO equations retain the formal structure of the classical Sn equations, they have a number of important differences. The LDO equations naturally allow the angular flux to be evaluated in directions other than those found in the quadrature set. To calculate the scattering source in the LDO equations, no spherical harmonic moments are needed—only values of the angular flux. Moreover, the LDO scattering source preserves the eigenstructure of the continuous scattering operator. The formal similarity of the LDO equations with the Sn equations should allow easy modification of mature three-dimensional Sn codes such as PARTISN or PENTRAN to solve the LDO equations. Numerical results are shown that demonstrate the spectral convergence (in angle) of the LDO equations for smooth solutions and the ability to mitigate ray effects by increasing the angular resolution of the LDO equations.