Abstract
Most of the neutron diffusion codes use numerical methods giving accurate results in
structured meshes. However, the application of these methods in unstructured meshes to
deal with complex geometries is not straightforward and it may cause problems of
stability and convergence of the solution. By contrast, the Finite Volume Method (FVM)
is easily applied to unstructured meshes and is typically used in the transport equations
due to the conservation of the transported quantity within the volume. In this paper, the
FVM algorithm implemented in the ARB Partial Differential Equations Solver has been
used to discretize the multigroup neutron diffusion equation to obtain the matrices of the
generalized eigenvalue problem, which has been solved by means of the SLEPc library.
Nevertheless, these matrices could be large for fine meshes and the eigenvalue problem
resolution could require a high calculation time. Therefore, a transformation of the
generalized eigenvalue problem into a standard one is performed in order to reduce the
calculation time.
