HP Finite element method for the simplified Pn equations

Abstract

[EN] The simplified spherical harmonics approximation to the neutron transport equation defines the neutron distribution inside a nuclear reactor core more accurately than the widely used neutron diffusion equation. To solve this equation, a goal oriented h-adaptable finite element method is employed. The proposed adaptive mesh refinement (AMR) method splits mesh cells whose errors are large and whose importance towards the computational goal is high. In this work, the computational goal is set as the maximum averaged power in an assembly of the reactor as this usually is a design constraint. The goal oriented error estimator is compared with the usual Kelly error indicator and also with a uniform global refinement. The goal oriented error estimator demonstrates to be the most accurate strategy in order to minimise the error in the defined quantity of interest and it is as much efficient as standard error estimators to compute the fundamental eigenvalue.