On solutions to the Pn equations for thermal radiative transfer
On solutions to the Pn equations for thermal radiative transfer
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DOI：
10.1016/j.jcp.2007.11.027
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发表时间：
2008-02-20
影响因子：
4.1
通讯作者：
Brunner, Thomas A.
中科院分区：
文献类型：
--
作者：
McClarren, Ryan G.;Holloway, James Paul;Brunner, Thomas A.
本文给出了用球谐函数（P-n）方法求解含时热辐射输运问题的结果。我们证明了一个定理，证明了在流动极限下，空间和时间连续的P-n方程对n的任何有限阶都允许负能量密度。我们还开发了一种隐式数值方法来求解P-n方程，以探索定理的影响。数值方法使用高分辨率的黎曼解算器产生一个迎风离散。我们采用了一个准线性的方法来整合的非线性添加，使计划的非振荡。我们使用向后欧拉方法的时间积分和处理的材料相互作用项完全非线性。反射边界条件的P-N方程，我们展示了如何实现这一边界条件使用鬼细胞。隐式方法能够产生强大的结果，在一个和两个维度的热传输问题。用数值方法分析了几个问题的不同P-n展开阶的精度。在二维问题中，数值P-n解包含负的辐射能量密度，正如我们的定理所预言的那样。数值结果表明，材料温度也变成了负值，这超出了定理的范围。我们的数值方法可以处理这些负值，但它们会在辐射流体力学计算中引起问题。爱思唯尔公司出版
We present results for the spherical harmonics (P-n) method for solving problems of time-dependent thermal radiative transport, We prove a theorem that demonstrates that in the streaming limit, the spatially and temporally continuous P-n equations will allow negative energy densities for any finite order of n. We also develop an implicit numerical method for solving the P-n equations to explore the impact of the theorem. The numerical method uses a high-resolution Riemann solver to produce an upwinded discretization. We employ a quasi-linear approach to integrate the nonlinearites added to make the scheme non-oscillatory. We use the backward Euler method for time integration and treat the material interaction terms fully nonlinearly. Reflecting boundary conditions for the P-n equations are presented and we show how to implement this boundary condition using ghost cells. The implicit method was able to produce robust results to thermal transport problems in one and two dimensions. The numerical method is used to analyze the accuracy of various P-n expansion orders on several problems. In two-dimensional problems the numerical P-n solutions contained negative radiation energy densities as predicted by our theorem. The numerical results showed that the material temperature also became negative, a result outside the scope of the theorem. Our numerical method can handle these negative values, but they would cause problems in a radiation-hydrodynamics calculation. Published by Elsevier Inc.