Asymptotic Analysis of a Computational Method for Time- and Frequency-Dependent Radiative Transfer
Asymptotic Analysis of a Computational Method for Time- and Frequency-Dependent Radiative Transfer
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DOI：
10.1006/jcph.1998.6063
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发表时间：
1998-10
影响因子：
4.1
通讯作者：
M. Adams;P. Nowak
中科院分区：
文献类型：
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作者：
M. Adams;P. Nowak
我们考虑了一个依赖时间、能量依赖的非线性辐射传输问题，其中不透明度大O(？1)，内源小O(？)]。通过对该问题的渐近分析，得到了系统内部的平衡扩散方程，以及该方程的边界条件和初始条件。我们将同样的渐近分析应用于离散形式的问题，其中频率变量用多群方法离散，方向变量用离散纵坐标方法离散，时间变量用全隐式方法离散，空间变量用亚格子平衡法离散。我们发现，当？？0时，离散解满足正确的平衡扩散方程的稳健离散化版本，且边界条件和初始条件非常精确。因此，分析预测，如果选择一种分解内部温度梯度的空间网格，那么即使空间单元的光学厚度趋于∞并且输运解中的边界层不被分辨，数值方法也能在系统内部获得精确解。我们进一步分析了在某些光子频率下光学很薄，而在另一些光子频率上很厚的问题，并再次表明离散解是非常准确的。我们给出了验证这些和其他分析预测的数值结果。
We consider a time-dependent, energy-dependent, nonlinear radiative transfer problem in which opacities are large O(??1)] and interior sources are small O(?)]. An asymptotic analysis of this problem as ??0 leads to the equilibrium diffusion equation in the interior of the system, along with boundary conditions and initial conditions for this equation. We apply the same asymptotic analysis to a discrete version of the problem, in which the frequency variable is discretized by the multigroup method, the direction variable by the discrete-ordinates method, the time variable by the fully implicit method, and the spatial variable by a subcell-balance method. We find that as ??0 the discrete solution satisfies a robust discretized version of the correct equilibrium diffusion equation, with boundary conditions and initial conditions that are remarkably accurate. The analysis thus predicts that if a spatial grid is chosen that resolves interior temperature gradients, then the numerical method obtains an accurate solution in the interior of the system, even though the optical thickness of the spatial cells tends to ∞ and boundary layers in the transport solution are not resolved. We go a step further to analyze problems that are optically thin at some photon frequencies but thick at others, and show that once again the discrete solution is remarkably accurate. We present numerical results that verify these and other predictions of the analyses.