Publications
Spherical harmonics (PN) methods in the sceptre radiation transport code
The SCEPTRE radiation transport code includes several methods for handling the angular dependence of the Boltzmann transport equation, including discrete ordinates (SN), spherical harmonics (PN) and angular finite elements. This paper presents three of the PN methods available in SCEPTRE: a first-order method using discontinuous spatial finite elements (DFE), a second- order method using continuous spatial finite elements (CFE), and a least-squares (LS) method, also using CFE. For the LS method, the effect of scaled weighting on the accuracy of the solution for diffusive systems is investigated. As in the SN method, vacuum (inflow) boundary conditions and source terms are specified at discrete directions. SN-space information is converted to moments-space information using a discrete-to-moment operator V. V may be either a standard one, i.e. one that includes a complete set of moments up to a given order, or it may be a Galerkin one, which provides a mapping from discrete-to-moment space and back again without loss of information. By using a Galerkin mapping, it is shown that the PN solver yields the same result as the corresponding SN solve (even including ray effects, if present in the 5N solution). The methods are applied to several test problems including a diffusive test, problems including isolated sources and voids, and electron emission from a thin wire in a void. The results are compared with converged deterministic results and Monte Carlo results.