Numerical Solution of the Time- and Space-Dependent Multigroup Neutron Diffusion Equations

Abstract

A numerical method for the solution of the time- and space-dependent multigroup diffusion equations is presented. The method permits a significant reduction in the computer time required to solve these equations by substantially increasing the allowable time step size. In the point reactor case, a form of the method considerably simplifies the calculation by removing the explicit dependence on the generation time and the delayed-neutron terms.The space-time equations are transformed into the Laplace domain and after multiplication by a weighting function they are transformed back into the time domain. By appropriate choice of the weighting function the equations appear either as coupled convolution integrals, where numerically difficult (e.g., generation time and delayed neutron) terms have been canceled, or as coupled integral equations in the weighted residual form, which permits very large time steps to be taken.