Richardson Extrapolation Applied to Difference Methods for Numerically Solving the Neutron Transport Equation in Spherical Geometry

Two new difference schemes are derived for numerically solving the transport equation in spherical geometry. The first difference method is positive; i.e., the calculated fluxes are never negative. Furthermore, for the first method, the error expansion is suitable for applying Richardson extrapolation with respect to both spatial and angular variables to increase the accuracy of the approximate fluxes. Numerical experiments illustrate the accuracy obtained using this procedure, as well as demonstrate that the accuracy of the second difference method is significantly improved through application of Richardson extrapolation. In addition, the numerical results indicate that the second method is significantly more accurate than the standard nonextrapolated diamond-difference method for numerically solving the transport equation in spherical geometry.