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 | 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
- Applied Mathematics
- Statistical and Nonlinear Physics
- Transportation
- General Physics and Astronomy
- Mathematical Physics