Abstract

We study the validity of the time-dependent asymptotic P_N approximation in radiative transfer of photons. The time-dependent asymptotic P_N is an approximation which uses the standard P_N equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic P_N approximation for radiative transfer requires careful treatment regarding the closure equation. Specifically, the mean number of particles that are emitted per collision (${\omega }_{\text{eff}}$) can be larger than one due to inner or outer radiation sources and the coefficients of the closure must be extended for these cases. Our approximation is tested against a well-known radiative transfer benchmark. It yields excellent results, with almost correct particle velocity that controls the radiative heat-wave fronts.

摘要

我们研究了时间相关渐近P _N近似在光子辐射传输中的有效性。瞬态渐近P _N是一种近似值，它使用标准P _N方程，其闭包基于精确玻尔兹曼方程在空间和时间上的齐次问题的渐近解。辐射传输的渐近P _N近似需要对闭合方程进行仔细处理。具体来说，每次碰撞发射的平均粒子数（${\omega }_{\text{效果}}$由于内部或外部辐射源， ) 可能大于 1，并且必须针对这些情况扩展闭包系数。我们的近似值根据众所周知的辐射传输基准进行了测试。它产生了极好的结果，几乎正确的粒子速度控制了辐射热波前沿。