Solving two-dimensional space-time dependent multi-group diffusion equations with SOR method

Abstract

In this research, solution of two-dimensional space-time diffusion equations with SOR (Successive Over Relaxation) method has been proposed. SOR method is chosen because this method is one of iterative methods that does not require to define whole element matrix. The results of this research have been compared with the results of TWIGL two-dimensional problems. The research is divided in two cases: homogeneous and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity, ramp reactivity and sinusoidal reactivity. Difference of thermal neutron flux varies with reactivity insertion in heterogeneous cases, although number of mesh and error tolerance is similar between step and ramp reactivity insertion cases. In general, the results of simulations are in agreement with data from reference. In the case of sinusoidal reactivity insertion, the pattern of flux distribution is repeated in interval of period with increased amplitude. SOR is an effective method to solve two-dimensional space-time multi-group diffusion equations.