Numerical analysis of step characteristic methods and computational comparison with step nodal methods in x, y geometry

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Abstract
We are pursuing a study of new numerical methods used to solve the x, y geometry discrete ordinates neutron transport equation. For both Ckl characteristic and Nkl nodal methods, the angular flux is approximated by a polynomial of total degree k inside each mesh cell and by polynomials of degree l along the cell edges. In this paper the convergence properties of the simplest methods of both families, i.e. the Ckl step characteristic and Nki step nodal schemes are investigated. On the one hand error bounds for a pure absorber calculation by the Ck0 characteristic methods are given. On the other hand experimentally observed errors and convergence rates are reported for the C00, C10, N00 and N10 schemes. It is proved that all the Ck0 methods are first order convergent in a discrete L2 norm. The numerical results confirm these theoretical estimations. In addition they indicate that the step nodal schemes are asymptotically second order convergent for unusually smooth data and solution, and asymptotically first order convergent for problems having realistic smoothness. Besides the step nodal methods are shown to significantly outperform the step characteristic methods in both cases.

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