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

Ansar Calloo, Jean-François Vidal, Romain Le Tellier, Gérald Rimpault

Nuclear Science and Engineering / Volume 180 / Number 2 / June 2015 / Pages 182-198

Technical Paper /

First Online Publication:May 5, 2015
Updated:May 29, 2015

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.

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