Positive linear and nonlinear surface characteristic schemes for the neutron transport equation in unstructured geometries

In this paper we present two new numerical schemes for the method of characteristic in unstructured geometries (MOC) for the neutron transport equation. The MOC has become a familiar tool for transport calculations in reactor physics [1], and its use will probably increase in the future. One of the major drawbacks of the MOC is the difficulty to implement higher-order integration schemes to improve spatial convergence. We present here two high-order schemes for the MOC, the second being a direct generalization of the first. We define a positive, linear characteristic scheme based on linear interpolation on the surface's values of the collisions sources. We have called it Linear Surface (LS) scheme. Results comparisons of the well-known Stepanek benchmark show LS faster convergence over the standard step characteristic scheme. A generalization of the synthetic ASA acceleration scheme provides an efficient method to accelerate the internal transport iterations. However, the LS scheme is not conservative. To improve this scheme we have adopted a nonlinear rebalancing procedure. The result is a Non-Linear Surface (NLS) scheme permitting linear variation of the source but also source discontinuities that enforce neutron conservation. The comparisons of the results for the Stepanek benchmark show that this method is much better with respect to spatial convergence. Unfortunately the nonlinear nature of the scheme complicates the conception of an acceleration method. (author)