强非均匀介质中离散坐标辐射转移方程的数值积分
Numerical integration of the discrete-ordinate radiative transfer equation in strongly non homogeneous media
摘要：
我们考虑辐射传递问题的离散纵坐标，平面平行的方法。我们介绍了两个基准问题的精确已知的解决方案，并表明，对于强非均匀介质的均匀层近似可以导致10%的误差估计的强度。我们提出并验证了一种通用的数值方法，将双边界问题转化为初始边界问题，使用自适应步长积分和局部光学性质的插值，可以提高两个数量级的解决方案的精度。这对于实际应用（例如大气辐射传输）来说也是令人感兴趣的，其中介质的散射和吸收特性随着高度而强烈变化，并且仅基于测量或模型在某些离散点处是已知的。
英文摘要：
We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers approximation can lead to errors of 10% in the estimation of the intensity. We propose and validate a general purpose numerical method that transforming the two-boundary problem into an initial boundary problem, using an adaptative step integration and an interpolation of the local optical properties, can improve the accuracy of the solution up to two orders of magnitude. This is furthermore of interest for practical applications, such as atmospheric radiation transfer, where the scattering and absorbing properties of the media vary strongly with height and are only known, based on measurements or models, at certain discrete points.
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