Nonnegative anisotropic group cross sections: A hybrid Monte Carlo-discrete elements-discrete ordinates approach

Conventional discrete ordinates transport calculations often produce negati ve fluxes due to unphysical negative scattering cross sections and/or as ar tifacts of spatial differencing schemes such as diamond difference. Inheren tly nonnegative spatial methods, such as the nonlinear, exponential charact eristic spatial quadrature, eliminate negative fluxes while providing excel lent accuracy, presuming the group-to-group, ordinate-to-ordinate cross sec tions are all nonnegative. A hybrid approach is introduced in which the flo w from spatial cell to spatial cell uses discrete ordinates spatial quadrat ures, while anisotropic scattering of flux from one energy-angle bin (energ y group and discrete element of solid angle) to another such bin is modeled using a Monte Carlo simulation to evaluate the bin-to-bin cross sections. The directional elements the the sphere of directions; the ordinates for th e spatial quadrature are at the centroids of the elements. The method is de veloped and contrasted with previous schemes for positive cross sections. A n algorithm for evaluating the Monte Carlo (MC)-discrete elements (MC-DE) c ross sections is described, and some test cases are presented. Transport ca lculations using MC-DE cross sections are compared with calculations using conventional cross sections and with MCNP calculations. In this testing, th e new method is about as accurate as the conventional approach, and often i s more accurate. The exponential characteristic spatial quadrature, using t he MC-DE cross sections, is shown to provide useful results where linear ch aracteristic and spherical harmonics provide negative scalar fluxes in ever y cell in a region.