The Asymptotic Telegrapher's Equation (P ₁) Approximation for Time-Dependent, Thermal Radiative Transfer

We develop the asymptotic P ₁ approximation for the time-dependent thermal radiative transfer equation for a multidimensional general geometry. Careful derivation of the asymptotic P ₁ equations, directly from the time-dependent Boltzmann equation, yields a particle velocity that is closer (v ≈ 0.91c) to the exact value of c but is based on an asymptotic analysis rather than diffusion theory (infinite velocity) or conventional P ₁ theory (which gives rise to the Telegrapher's equation, v= 1/√3c ≈ 0.577c). While this approach does not match the exact value of c as does the P _1/3 method, the latter method is an ad hoc approach that has not been justified on theoretical grounds. This article provides the theoretical justification for the almost-correct value of c that yields improved results for the well-known (one-dimensional) Su-Olson benchmark for radiative transfer, for which we obtain a semi-analytic solution in the case of local thermodynamic equilibrium. We found that the asymptotic P ₁ approximation yields a better solution than the diffusion, the classic P ₁, and the P _1/3 approximations, yielding the correct steady-state behavior for the energy density and the (almost) correct particle velocity.