On the Accuracy of Transport Spatial Discretization Methods for Diffusive Regimes

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An infinite-medium analysis is performed for neutron transport spatial discretization methods in planar geometry. Angular flux solutions of the spatially continuous transport equation, which are driven by a linear (or quadratic) source, are shown to vary linearly (or quadratically) in space and angle; these are used to assess whether the discretized transport equations preserve certain cell-averaged and edge quantities. Each of the continuous angular flux solutions has a scalar flux that satisfies the standard diffusion equation; our analysis predicts whether the transport discretizations yield an accurate diffusion coefficient and (diffusion) spatial differencing scheme. The linear moment–based discretization methods under consideration, which are found to preserve certain features of the linear (or quadratic) infinite-medium angular flux solutions, are the familiar linear discontinuous (LD), lumped linear discontinuous (LLD), and linear characteristic (LC) schemes. The step characteristic scheme, which yields an unphysically large diffusion coefficient, is revisited and shown to possess, for diffusive problems, a solution error that would occur if an unphysical anisotropic scattering term had been included in the starting discretized S N transport equations. The numerical results verify the theoretical predictions and demonstrate the accuracy of the LD, LLD, and LC schemes in highly scattering problems that are optically thick. Our numerical results also illustrate the impact of inaccuracies in the diffusion coefficient on the numerical solutions of eigenvalue problems. The analysis in this paper has practical implications in the choice of spatial schemes used to solve realistic eigenvalue problems.