Heterogeneous nuclear reactors require numerical methods to solve the neutron diffusion equation (NDE)
to obtain the neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of
homogeneous regions. This discretization requires additional equations at the inner faces of two adjacent
cells: neutron flux and current continuity, which imply an excess of equations. The finite volume method
(FVM) is suitable to be applied to NDE, because it can be easily applied to any mesh and it is typically
used in the transport equations due to the conservation of the transported quantity within the volume.
However, the gradient and face-averaged values in the FVM are typically calculated as a function of the
cell-averaged values of adjacent cells. So, if the materials of the adjacent cells are different, the neutron
current condition could not be accomplished. Therefore, a polynomial expansion of the neutron flux is
developed in each cell for assuring the accomplishment of the flux and current continuity and calculating
both analytically. In this polynomial expansion, the polynomial terms for each cell were assigned previously
and the constant coefficients are determined by solving the eigenvalue problem with SLEPc. A sensitivity
analysis for determining the best set of polynomial terms is performed.This work has been partially supported by the Spanish Ministerio de Eduacion Cultura y Deporte [grant number FPU13/01009]; the Spanish Ministerio de Ciencia e Innovacion [project number ENE2014-59442-P], [project number ENE2012-34585]; the Generalitat Valenciana [project number PROMETEOII/2014/008]; the Universitat Politecnica de Valencia [project number UPPTE/2012/118]; and the Spanish Ministerio de Economia y Competitividad [project number TIN2013-41049-P].Bernal García, Á.; Román Moltó, JE.; Miró Herrero, R.; Ginestar Peiro, D.; Verdú Martín, GJ. (2016). Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation. Journal of Nuclear Science and Technology. 53(8):1212-1223. https://doi.org/10.1080/00223131.2015.1102661S1212122353
