The Asymptotic Telegrapher’s Equation (P1) Approximation for Time-Dependent, Thermal Radiative Transfer

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. We develop the asymptotic P 1 approximation for the time-dependent thermal radia-tive 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 radia-tive transfer, for which we obtain a semi-analytic solution in the case of local thermo-dynamic 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.