An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations
An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations
复制标题
频率相关辐射传递方程的渐近保持统一气体动力学格式
DOI：
10.1016/j.jcp.2015.09.002
复制
发表时间：
2015-12
影响因子：
4.1
通讯作者：
Li Shu
中科院分区：
文献类型：
--
作者：
Sun Wenjun;Jiang Song;Xu Kun;Li Shu
本文提出了以前工作的扩展（Sun等人，2015 [22]）的灰色辐射传输方程的统一气体动力学方案（UGKS）的频率相关（多组）辐射传输系统。与灰度辐射传输方程不同，其中光学不透明度仅是局部材料温度的函数，与频率相关的辐射传输的模拟与来自频率相关的不透明度的额外困难相关联。对于多频辐射，不透明度取决于空间位置和频率。例如，不透明度通常是频率的递减函数。在相同的空间区域，输运物理对于低频光子可以是光学厚的，而对于高频光子可以是光学薄的。因此，光学厚度不是空间位置的简单函数。本文发展了适用于频率相关辐射系统的UGKS。UGKS方法是一种有限体积方法，其输运物理模型是根据光子频率依赖的平均自由程与胞大小的比值来建立的，当胞大小远大于光子的平均自由程时，可以得到这种频率辐射的扩散解。另一方面，当细胞的大小是远远小于光子的平均自由程，一个自由的传输机制将恢复。在上述两个极限之间的区域，随着局域胞大小与光子平均自由程之间的比率的变化，UGKS提供了在物理和频率空间中的平滑过渡，以准确地捕获相应的输运物理。UGKS从灰色到多频辐射系统的看似简单的扩展是由于其内在一致的多尺度传输模型，但它仍然涉及大量的工作，以适当地离散多个组，以设计一个渐近保持（AP）计划在所有政权。在几个与频率有关的辐射问题中对该格式进行了测试，并将结果与隐式蒙特卡罗方法的结果进行了比较。UGKS比IMC更有效，并且列出了所有测试用例的两种方案的计算时间。该UGKS似乎是第一个离散纵标方法（DOM）的准确捕获的多频辐射输运物理从弹道粒子运动的扩散波传播。
This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP) scheme in all regimes. The current scheme is tested in a few frequency-dependent radiation problems, and the results are compared with the solutions from the well-defined implicit Monte Carlo (IMC) method. The UGKS is much more efficient than IMC, and the computational times of both schemes for all test cases are listed. The UGKS seems to be the first discrete ordinate method (DOM) for the accurate capturing of multiple frequency radiative transport physics from ballistic particle motion to the diffusive wave propagation.
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DOI：
--
发表时间：
2014-05
期刊：
arXiv: Numerical Analysis
影响因子：
--
作者：
Chang Liu;K. Xu;Quanhua Sun;Q. Cai
通讯作者：
Chang Liu;K. Xu;Quanhua Sun;Q. Cai
DOI：
10.1142/s0218202501001082
发表时间：
2001-07
影响因子：
3.5
作者：
A. Klar;C. Schmeiser
通讯作者：
A. Klar;C. Schmeiser
影响因子：
2.9
作者：
A. Klar
通讯作者：
A. Klar
影响因子：
4.1
作者：
M. Adams;P. Nowak
通讯作者：
M. Adams;P. Nowak
影响因子：
4.1
作者：
E. Larsen
通讯作者：
E. Larsen