Analytical technique of multi-energy groups point kinetics model for multidimensional homogeneous reactors

Abstract The solution of the balancing equation of the neutron flux coupled with the delayed neutron precursor concentrations is the fundamental neutronic problem of any transient analysis. A finite difference solution to a two- or three-dimensional dynamics issue necessitates an incredibly high number of calculations, highlighting the need for more straightforward approaches that may be used effectively in ordinary studies. The point reactor model, discussed and used in numerous literature, is the simplest of these techniques. This paper provides an analytical technique for the multi-energy groups point kinetics model, which is at the core of multidimensional homogeneous reactors. Furthermore, like with the quasi-static method, this analytical technique is based on variable separation, and a matrix approach is used to formulate the stiff coupled differential equations system. The exponential function of a coefficient matrix can be represented as a polynomial function with variable coefficients. These coefficients can be determined analytically by utilizing the eigenvalues of the coefficient matrix. The suggested method applies to 2D and 3D homogeneous reactors with various forms of linear, sinusoidal, and pulse reactivity, including nonlinear reactivity, through temperature feedback. The numerical data comparison using analytical methods enhanced accuracy and efficacy, showing strong agreement with conventional and benchmark techniques.