Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry

• The simulation of transients on nuclear reactors involving control rods movements present the rod-cusping problem.
• To avoid this problem, a moving mesh scheme based on hp-finite element method is proposed for the time dependent neutron diffusion equation.
• 1D and 3D benchmarks have been studied obtaining accurate results for coarse mesh discretizations.

To simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time-dependent neutron diffusion equation inside the reactor core. Here the spatial discretization of this equation is done using a finite element method that permits h–p   refinements for different geometries. This means that the accuracy of the solution can be improved refining the spatial mesh (hh-refinement) and also increasing the degree of the polynomial expansions used in the finite element method (pp-refinement). Transients involving the movement of the control rod banks have the problem known as the rod-cusping effect. Previous studies have usually approached the problem using a fixed mesh scheme defining averaged material properties. The present work proposes the use of a moving mesh scheme that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells. The performance of the moving mesh scheme is tested studying one-dimensional and three-dimensional benchmark problems.