A polynomial expansion method based on Helmholtz equation for the Neutron Diffusion Equation discretized by the Finite Volume Method

Autores UPV
Año
CONGRESO A polynomial expansion method based on Helmholtz equation for the Neutron Diffusion Equation discretized by the Finite Volume Method

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.