Numerical solution of the neutron diffusion equations as eigenvalue problem in the nuclear reactors using GDQ method

Abstract

The most widely used mathematical description of the neutron distribution in nuclear reactors is provided by neutron diffusion theory. If fission source does not balance the leakage and absorption terms, to use steady state diffusion equation we multiply the source term by a constant 1/k, where k is multiplication factor. The equation may be rewritten as an eigenvalue equation. In this paper, Generalised Differential Quadrature (GDQ) method is presented to solve the multi-groups neutron diffusion equations for nuclear reactors as an eigenvalue problem. The main idea of the GDQ is that the derivative of a function at a sample point can be approximated as a weighted linear summation of the value of the function at all of the points in the domain. The comparison between GDQ and Finite Difference (FD) methods shows a significant improvement in the convergence rate for GDQ method with a smaller number of grid points.