Second-order time evolution of PN equations for radiation transport

Using polynomials to represent the angular variation of the radiation intensity is usually referred to as the PN or spherical harmonics method. For infinite order, the representation is an exact solution of the radiation transport solution. For finite N, in some physical situations there are oscillations in the solution that can make the radiation energy density be negative. For small N, the oscillations may be large enough to force the material temperature to numerically have non-physical negative values. The second-order time evolution algorithm presented here allows for more accurate solutions with larger time steps; however, it also can resolve the negativities that first-order time solutions smear out. Therefore, artificial scattering is studied to see how it can be used to decrease the oscillations in low-order solutions and prevent negativities. Small amounts of arbitrary, non-physical scattering can significantly improve the accuracy of the solution to test problems. Flux-limited diffusion solutions can also be improved by including artificial scattering. One- and two-dimensional test results are presented.