梯度折射率介质内瞬态辐射传递的扩散近似法  

Diffusion Approximation Method for Transient Radiative Transfer in a Gradient Index Medium

作　　者：刘立君[1] 石弘 张一帆 刘晓燕[1] LIU Li-jun;SHI Hong;ZHANG Yi-fan;LIU Xiao-yan(School of Civil Engineering, Northeast Petroleum University, Daqing 163318, China)

机构地区：[1]东北石油大学土木建筑工程学院

出　　处：《数学的实践与认识》2018年第8期173-179,共7页Mathematics in Practice and Theory

摘　　要：基于瞬态时域与频域扩散近似方程求解了一维梯度折射率介质内辐射传递问题.通过计算在不同梯度折射率分布下的穿透率与反射率,对扩散近似的适用性展开研究.结果表明：求解时域穿透率时,扩散近似法始终能够准确计算出平行光的时间延迟,而对漫射部分时间延迟的计算不准确;对时域反射率而言,扩散近似法在反射率出现峰值之前与间断有限元法结果相吻合,随着折射率梯度的增大,扩散近似结果在出现峰值后的时间内偏大,且有明显的时移.对于频域穿透率和反射率计算,扩散近似法精度几乎不受折射率梯度变化的影响,能够较为准确地预测频域穿透率,但是对于频域反射率计算误差较大.In this paper, the dex media is solved based on radiative transfer problem the transient time-domain in one-dimensional gradient in- and frequency-domain diffusion approximation equations.The applicability of the diffusion approximation is investigated by calculating the transmittance and reflectivity signals at different gradient refractive index profiles. The results show that the solution of time domain penetration, diffusion approximation method is able to accurately calculate the parallel light time delay, and the calculation of the diffusion part time delay is not accurate; the time domain reflectivity, diffusion ap- proximation method before peak in reflectance and the discontinuous finite element method agree well with the increase of the refractive index gradient, diffusion approximation the results appear in the peak time is too large, and there is a clear shift. Spectral transmittance and reflectance calculation for diffusion approximation method, the accuracy is almost not affected by the refractive index gradient, can accurately predict the frequency penetration, but reflectivity large calculation error in frequency domain.

关 键 词：瞬态辐射 梯度折射率 扩散近似 频域 

分 类 号：TN24[电子电信—物理电子学]