Abstract
The neutron diffusion equation is an integral-differential equation which is used to
determine the power in nuclear reactors, which is crucial in nuclear safety analysis [1].
Since nuclear reactors are heterogeneous, geometrical discretization and numerical
methods are required to solve this equation. In particular, the Finite Volume Method can
be applied to this equation and it is suitable for fine meshes [2]. Moreover, a polynomial
expansion method can be used to obtain accurate results for coarse meshes to accelerate
the calculation [3]. By means of this method, the neutron flux is expanded in each cell
of the discretized geometry, as a sum of a finite set of polynomial terms, which are
assigned previously and their constant coefficients are determined by solving the
eigenvalue problem by means of SLEPc [4]. In this polynomial expansion method, it
was demonstrated that only one and four sets of basic polynomial terms give
appropriate results for meshes composed of hexahedra and tetrahedra respectively. In
this work, another set of polynomial terms, which are obtained by applying the
Helmholtz equation to the 3D neutron flux expansion, are used to obtain better results in
coarser meshes to accelerate the calculation.
