Numerical simulation of the nuclear reactors kinetics behavior using method of lines based on the GDQ method

In this paper, for the first time, numerical technique using Method of Lines (MOL) based on the Generalized Differential Quadrature method (GDQ) is developed and applied for two energy groups of reactor kinetics and one group of precursor delayed neutrons. Also, the presented method (MOL-GDQ) has been developed for 3D transient benchmark nuclear reactor with two neutron energy groups and six delayed precursor groups. The basic idea of the MOL is to replace the spatial (boundary value) derivatives in the Partial Differential Equations (PDE) with algebraic approximations. In other words, with only one remaining independent variable, we have a system of Ordinary Differential Equations (ODEs) that approximates the original PDE. The advantages of the GDQ method lie in its easy use and flexibility with regard to arbitrary grid spacing. Compared to the conventional low-order numerical techniques such as the finite element and finite difference methods, the GDQ method can yield accurate solutions with relatively much fewer grid points. The numerical technique is applied to three-dimensional space-time neutron diffusion equations with average one group of delayed neutrons in the different nuclear reactors. Also, the presented method (MOL-GDQ) is developed for 3D transient benchmark nuclear reactor with two neutron energy groups and six delayed precursor groups. Simulation results are presented to demonstrate the effectiveness of the proposed method in terms of performance and stability. The results of numerical technique are discussed and compared with the results of traditional methods and strong citations to demonstrate the accuracy of it.