On the importance of effective convergence velocity of synthetic acceleration methods in neutron transport

The present work concerns some aspects of the optimization of the synthesis acceleration techniques in neutron transport. The importance of non-asymptotic convergence velocity as a theoretical means to characterize and optimize acceleration methods is discussed in detail for isotropic as well as highly anisotropic scattering cases; this shows the innacuracy of results based only on the usual asyptotic analysis. A detailed study of convergence velocity behaviour for space discretized schemes and multidimensional problems is also presented. Finally, various kinds of theoretically-evaluated convergence velocities are reported to study the effective behaviour of some modifications of the classic DSA technique recently proposed to face its loss of effectiveness and optimize performances when dealing with highly anisotropic scattering; comparisons with results of already assessed DSA modification techniques are reported for various scattering cross-section configurations.