Analytic P1 solutions for time-dependent, thermal radiative transfer in several geometries

We present several solutions for the time-dependent P1 approximation (telegrapher's equation) coupled to thermal radiative transfer with Cv∝T3. Our solutions are based on the energy density Green's function in slab geometry, which we derive exactly. The analytic P1 solution is compared with analytic transport and diffusion solutions on one of the Su-Olson benchmark problems. Also, we transform the slab geometry Green's function into the solution from a point source (the 1D spherical Green's function) and an infinite line source (the 1D cylindrical Green's function). We evaluate the P1 solution to the line source and compare the result with a solution generated by a Pn numerical method.