The improved differential approximation for radiative transfer in multidimensional media
The improved differential approximation for radiative transfer in multidimensional media
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DOI：
10.1115/1.2910468
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发表时间：
1990-08
影响因子：
--
通讯作者：
M. Modest
中科院分区：
文献类型：
--
作者：
M. Modest
一种特别流行的近似方法是所谓的微分近似或P-1近似。不幸的是，微分近似仅在光学厚介质中是准确的，并且在光学薄的情况下可能变得非常不准确，特别是在二维和三维几何形状中。为了提高准确性，已经提出了一些改进。Olfe（1967，1968）在他所谓的修正微分近似（MDA）中将壁发射与介质发射分开。Modest（1974，1975）将P-1近似与光学薄修正项结合在一起，称为改进的微分近似（IDA）。虽然非常准确，但这两种模型都局限于相对简单的情况。最近，Modest（1989）证明了Olfe的MDA可以被公式化用于一般的三维情况，其中吸收/发射、各向异性散射介质由灰色、漫发射和反射壁限定。本说明的目的是表明，IDA也可以扩展到最一般的情况下，减少到正确的光学薄和光学厚的限制，为所有情况下，导致类似于MDA的精度，但计算更有效。
One particularly popular approximate method for radiative transfer in participating media is the so-called differential approximation or P-1 approximation. Unfortunately, the differential approximation is accurate only in optically thick media, and may become very inaccurate in optically thin situations, in particular in two- and three-dimensional geometries. To increase the accuracy, a number of improvements have been proposed. Olfe (1967, 1968) separated wall emission from medium emission in what he called the modified differential approximation (MDA). Modest (1974, 1975) combined the P-1 approximation with an optically thin correction term in what he called the improved differential approximation (IDA). While very accurate, both models were limited to relatively simple situations. Recently, Modest (1989) demonstrated that Olfe's MDA may be formulated for a general three-dimensional case with an absorbing/emitting, anisotropically scattering medium bounded by gray, diffusely emitting and reflecting walls. It is the purpose of the present note to show that the IDA may also be extended to the most general case, reducing to the correct optically thin and optically thick limits for all situations, resulting in accuracy similar to that of the MDA, but being computationally more efficient.