A solution of the multigroup transport equation using spherical harmonics

Abstract The flux φ(r,Ω) at location r in the direction of unit vector Ω is expanded as a series of the form where Pm l(cosθ) are associated Legendre polynomials of order L, m y with ψlm(r) and γlm(r) the coefficients or moments of the series and θ and φ the axial and azimuthal angles respectively of ω. Second order differential equations for ψlm(r) and γlm(r) result when odd l. terms are eliminated from the basic system obtained by substituting the series in the transport equation and these are solved numerically by finite difference or finite element techniques. N specifies the order of the approximation, denoted by PN. Following a summary of the method the paper describes two recent developments, firstly the treatment of anisotropic scatter, with preliminary results, and secondly an efficient means of dealing with vacuum boundary conditions for arbitrary surfaces.