Optimization Study on the Diffusion Synthetic Acceleration Algorithm in Three-Dimensional Discrete Ordinate Transport

This report provides a practical procedure to solve the diffusion synthetic acceleration (DSA) method in the three-dimensional discrete ordinate transport equation with the least computational time and hardware requirement. A study was made on the stability of the algorithm and it was found that the cause of the instability is strongly related to the coexistence of the plus and minus terms in the external source. A new procedure, plus and minus term separation, is proposed to ensure the unconditional stability, in which procedure the plus and minus terms are solved independently and then both solutions are added together to get the final solution. In order to enhance the convergence, an optimized SOR (successive over-relaxation) procedure was also investigated and applied to the method. This method provides a fully automatic optimization that ensures the best convergence in DSA process. The present method was encoded to a three-dimensional code TRITAC, and its efficiency was validated by numerical experiments on fast reactor calculations. 'The required number of S, and DSA sweeps were reduced by 40% and 65% respectively by the present method.'