Solution of some 2D transport problems by a high order AN–SP2N−1 method

A collection of classical 2D transport problems (the escape probability from prisms of various shapes, the current-to-flux ratio of a wedge-shaped reflector, the transport and asymptotic flux as well as the extrapolation length near a corner) are solved by means of the boundary element version of a high order AN method, an equivalent form of the odd order simplified spherical harmonics (SP2N−1) method. The use of a high order approximation is motivated by the fact that all the above problems can be made to fulfil the condition of constant total mean free path, which makes AN–SP2N−1 to be equivalent, in turn, to the classical odd order spherical harmonics (P2N−1) method, so that for these problems AN–SP2N−1 shares with the latter method the property that, by increasing the order 2N − 1, the error can be made as small as we want. A second purpose of the paper is to show that the boundary element approach can handle such highly singular boundary integrals as those implied by the partial derivatives of the asymptotic flux at the boundary.