Validation of the Legendre Expansion of the Collision Law for Light Water Reactor Calculations

In reactor physics, calculation schemes with deterministic codes are validated with respect to a reference Monte Carlo code. The remaining biases are attributed to the approximations and models induced by the multigroup theory (self-shielding models and expansion of the scattering law on Legendre polynomials) to represent physical phenomena (resonant absorption and scattering anisotropy). This work focuses on the relevance of a polynomial expansion to model the scattering law. Since the outset of reactor physics, the latter has been expanded on a truncated Legendre polynomial basis. However, the transfer cross sections are highly anisotropic, with nonzero values for a small range of the scattering angle. The finer the energy mesh and the lighter the scattering nucleus, the more exacerbated is the peaked shape of these cross sections. As such, the Legendre expansion is less well suited to represent the scattering law. Furthermore, this model induces negative values, which are nonphysical. Piecewise-constant functions have been used to represent the multigroup scattering cross section. This representation requires a different model for the diffusion source. Thus, the finite-volume method for angular discretization has been developed and implemented in the PARIS environment. This method is adapted for both the Legendre moments and the piecewise-constant functions representations. It provides reference deterministic results that validate the standard Legendre polynomial representation with a P3 expansion.