\section{Fuel assembly models description}
The model of the fuel assembly consists of the hexagonal lattice of fuel pins encased in the steel wrapper and cooled by LBE.
Each fuel pin contains the MOX fuel and the steel cladding and the gap of neutron gas.
A schematic view of the simulated FA is shown in Fig. \ref{fig:fa2dsketch}.\\
\begin{figure}[h]
\centering
\includegraphics[width=0.75\textwidth]{images/plots/pics/fa2d.png}
\caption{Cross sectional view of the MYRRHA fuel assembly}\label{fig:fa2dsketch}
\end{figure}

\textit{2D FA model}\\
The 2D FA model makes use of reflective boundary conditions in all directions assuming to model the FA as an infinite system. In the radial direction the assumption implies that the fuel assembly is completely surrounded by other FAs and therefore there is no neutron leakage since the neutrons crossing the boundary re-enter the system.\\

\textit{Homogeneous 3D FA model}\\
The 3D FA model considers a realistic fuel assembly design in which each fuel pin as a stack of fuel pellets, reflectors, a steel structure and plugs. The top and bottom grids and the supporting structures made of stainless steel are also modelled.
Such a model of the fuel assembly includes the neutron leakage from the axial boundaries, the neutron slowing down and the neutron reflection from above and below the FA active region.
In the homogeneous model fuel is considered as a whole for depletion calculation and the flux to estimate the reaction rates is averaged on the total fuel region.\\

\textit{3D FA model with depletion zones}\\
 To take into account a impact of axial dependant depletion the fuel material is divided in sub-zones where the respective reaction rates are evaluated taking the flux averaged on the specific regions.\\
 
\textit{Simulation setup}\\
%, a Monte Carlo burn-up code offering several advantages with respect to MCNP such as the reduced running time and the built-in depletion solver.
%The possibility to divide a burnable material in sub-zones is implemented in the code by the use of the card $div$ but it leads to an increase of the computational cost.
The simulation setup of the Serpent FA models is summarized in Tab. \ref{tab:serpent}.
\begin{table}[h]
\centering
\caption{Serpent simulation parameters}\label{tab:serpent}
\scalebox{0.7}{

\begin{tabular}{lrrrr}
\toprule
\textit{Model}       &   \makecell{Number of particles \\ simulated}     &    \makecell{Number active \\ generations }     &    \makecell{Predictor corrector}     &    \makecell{Simulation \\ running time}\\
\midrule
\textbf{2D accurate} &   1e5 &   250 &   CE-LI &   87 min\\
\textbf{2D simplified} &   1e4 &   250 &   No &   17 min\\
\textbf{3D homogeneous}     &   1e5 &   250 &   No &   83 min\\
\textbf{3D axial depletion (40 zones)}     &   1e5 &   250 &   No &   490 min\\

\bottomrule
\end{tabular}
}

\end{table}
For the accurate 2D FA model one of the available predictor-corrector schemes provided by Serpent is employed. CE-LI method, constant-extrapolation linear-interpolation is based on the calculation of flux and cross section at the beginning of the step and then the same calculation at the end of the step after the material is depleted. The final burnup calculation is performed linearly interpolating the values of flux and cross sections from the beginning to the end of the step.      