Cross sections polynomial axial expansion within the APOLLO3 3D characteristics method

A polynomial expansion for cross sections has been introduced in the 3D Method Of Characteristics (MOC) solver of the APOLLO3 code, with the aim of applying the method to depleted systems. This paper addresses the suitable adaptation of the MOC equations with regards to the free and DPN-accelerated power iterations, describing also how the conceived algorithms take advantage of a vectorized implementation. An adaptive quadrature technique is presented, necessary for the evaluation of terms that, due to the polynomial description, cannot be solved analytically. The decisive advantage of the new method over a classical step-constant description of nuclear properties is assessed by comparing the results of the depletion study of a PWR assembly.