Asymptotic analysis of the several competitive equations to solve the time-dependent neutron transport equation

摘要

Using conventional diffusion limit analysis, we asymptotically compare three competitive time-dependent equations (the telegrapher's equation, the time-dependent Simplified P(sub 2) (SP(sub 2)) equation, and the time-dependent Simplified Evcn-Parity (SEP) equation). The time-dependent SP(sub 2) equation contains higher order asymptotic approximations of the time-dependent transport equation than the other equations in a physical regime in which the time-dependent diffusion equation is the leading order approximation. In addition, we derive the multigroup modified time-dependent SP(sub 2) equation from the multigroup time-dependent transport equation by means of an asymptotic expansion in which the multigroup time-dependent diffusion equation is the leading, order approximation. Numerical comparisons of the timedependent diffusion, the telegrapher's, the time-dependent SP(sub 2), and S(sub 8) solutions in 2-D X-Y geometry show that, in most cases, the SP(sub 2) solutions contain most of the transport corrections for the diffusion approximation.