Keywords: time-dependent diffusion, backward finite difference scheme, Gauss-Seidel iteration, convergence, reactivity accidents, neutron diffusion equation, delayed neutron precursor equation, heat transfer, nuclear reactors, simulation, nuclear accidents
Numerical method for solving the three-dimensional time-dependent neutron diffusion equation
A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme.