A ROBUST SECOND-ORDER MULTIPLE BALANCE METHOD FOR TIME-DEPENDENT NEUTRON TRANSPORT SIMULATIONS

A second-order “Time-Dependent Multiple Balance” (TDMB) method for solving neutron transport problems is introduced and investigated. TDMB consists of two coupled equations: (i) the original balance equation (the integrated over a time step) (ii) “balance-like” auxiliary (an approximate equation). Simple analysis shows that accurate robust (unconditionally free from spurious oscillation). source iteration (SI) with diffusion synthetic acceleration (DSA) formulated to solve these equations. Fourier reveals convergence rates proposed schemes are similar those common (SI + DSA) Backward Euler (BE); however, requires about twice computational effort per iteration. To demonstrate theory—accuracy, robustness, rate—and investigate efficiency TDMB, we present results discrete ordinates (Sn) research code. Results discussed, future work proposed.