## Abstract

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.

Original language | American English |
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Pages (from-to) | 175-199 |

Number of pages | 25 |

Journal | Transport Theory and Statistical Physics |

Volume | 41 |

Issue number | 3-4 |

DOIs | |

State | Published - May 2012 |

Externally published | Yes |

## Keywords

- Boltzmann equation
- diffusion equation
- kinetic theory
- radiative transfer
- transport theory

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Transportation
- Physics and Astronomy(all)
- Applied Mathematics

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