Development of a diffusive simplified double P[formula omitted] approximation to the neutron transport equation

Abstract

The neutron transport equation models the distribution of the neutron power inside a reactor core. The complexity of integrating this equation implies the use of some angular approximations. Discrete ordinates and spherical harmonics equations (PN equations) are commonly used to this purpose, but even when these approaches are used, the resulting set of equations requires high computational demands. An alternative is to develop simplified formulations of them, such as the simplified spherical harmonics equations (SPN equations), which provide accurate results. The spherical harmonic equations are based on the regularity of solution in terms of the angular dependence. However, in some reactor configurations, the angular fluxes can be discontinuous. For that, the double spherical harmonics equations, where angular fluxes are expanded in terms of two sets of Legendre polynomials, were studied. In this work, a simplified treatment of them is developed that leads to a diffusive set of equations, the simplified double spherical harmonics equation (SDPN equations). Numerical results show that the SDPN approximation provides faster and more accurate results than the SPN equations for some problems with strong variations of the angular neutron flux.