Application of the galefxin finite element method to reactor dynamic problems

Abstract

Abstract The method of Galerkin is used to obtain a semidiscrete formulation of the time-dependent multigroup diffusion equa-tions which are then integrated in time by the θ-method to obtain a system of algebraic equations. For given initial and boundary conditions, successive estimates of the neutron flux for each energy group and the precursor concentrations for each delayed neutron group are obtained. Since the precursor concentrations are not necessarily continuous across an interface, the global basis functions are treated in a different form than the corresponding ones for the neutron flux. A computer code is implemented using quadratic Lagrange basis functions. Numerical results for a one-dimensional subcritical transient problem show that this method is as accurate as the usual finite difference schemes but considerably more efficient.