Asymptotic derivation and numerical investigation of time-dependent simplified PNPN equations

The steady-state simplified PNPN (SPNSPN) approximations to the linear Boltzmann equation have been proven to be asymptotically higher-order corrections to the diffusion equation in certain physical systems. In this paper, we present an asymptotic analysis for the time-dependent simplified PNPN equations up to N=3N=3. Additionally, SPNSPN equations of arbitrary order are derived in an ad hoc way. The resulting SPNSPN equations are hyperbolic   and differ from those investigated in a previous work by some of the authors. In two space dimensions, numerical calculations for the PNPN and SPNSPN equations are performed. We simulate neutron distributions of a moving rod and present results for a benchmark problem, known as the checkerboard problem. The SPNSPN equations are demonstrated to yield significantly more accurate results than diffusion approximations. In addition, for sufficiently low values of N  , they are shown to be more efficient than PNPN models of comparable cost.