A Laplace transform exponential method for monoenergetic three-dimensional fixed source discrete ordinates problems in Cartesian geometry
We describe a Laplace transform exponential method applied to x-y-z geometry heterogeneous neutron transport problems in the discrete ordinates (SN) formulation that we refer to as the LTSN – Exp method. This numerical method uses the space Laplace transform technique to solve the one-dimensional transverse-integrated SN exponential equations within one of the homogeneous regions of the domain of solution. Based on the physics of shielding problems where the neutron flux attenuates exponentially with increasing distance from the source, we approximate the transverse leakage terms by exponential functions. We show in two numerical experiments that the LTSN – Exp method generates very accurate results in highly absorbing media.
Keywords: Laplace transform, LTSN-Exp method, discrete ordinates, neutron transport problems, transverse leakage