Computation accuracy and efficiency of a power series analytic method for two- and three- space-dependent transient problems

The establishment of solutions to large-scale three-dimensional (3-D) reactor benchmark problems is needed to serve as standards for the verification of design codes and for the detailed error analysis of calculational methods. A number of partially and fully inserted control rods, represented by absorber added to certain subassemblies, cause a strong nonseparable power distribution. In addition, the existence of a very large thermal flux peak in the reflector makes this a very difficult and challenging problem to solve.PWS code has been developed to include a numerical solution for the time-dependent neutron diffusion equations for the nuclear reactor analysis. The new technique employs a new parameter (α) which can reduce the rapid increase in magnitude of the power series coefficients. These coefficients, in turn, are determined by back substitutions in the non-linear canonical diffusion equations and treating terms of the same degree to obtain a modified recurrence relation which is valid for any type of the stiff non-linear kinetic diffusion equations.The validity of the algorithm was tested with three kinds of well-known two-group benchmark problems. The first one is the two-dimensional TWIGL seed-blanket reactor kinetics problem. The second is the two- and three-dimensional LAR BWR benchmark problem simulating a rod drop accident of a BWR core. The third is the three-dimensional LMW LRA transient problem which simulates an operational transient involving rod movements. The obtained results with the proposed PWS code are compared with those provided by other reference codes, indicating an overall agreement and excellent performance.