Convergence of filtered spherical harmonic equations for radiation transport
Convergence of filtered spherical harmonic equations for radiation transport
复制标题
辐射传输滤波球谐方程的收敛性
DOI：
10.4310/cms.2016.v14.n5.a10
复制
发表时间：
2016
影响因子：
1
通讯作者：
Kerstin Küpper
中科院分区：
文献类型：
--
作者：
M. Frank;C. Hauck;Kerstin Küpper
我们分析了辐射传输的滤波球谐函数 (FPN) 方程的全局收敛特性。众所周知的球谐函数 (PN ) 方程是辐射传输方程的谱方法（角度），并且已知会受到不连续性周围吉布斯现象的影响。滤波方程包括通过光谱滤波过程导出的附加项来解决这个问题。我们明确地展示了谱方法对输运方程解的全局 L2 收敛速度（在空间和角度上）如何取决于解的平滑度（仅在角度上）和滤波器的阶数。结果通过数值实验得到证实。数值测试已在 MATLAB 中实现并可在线获取。
We analyze the global convergence properties of the filtered spherical harmonic (FPN ) equations for radiation transport. The well-known spherical harmonic (PN ) equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the global L2 convergence rate (in space and angle) of the spectral method to the solution of the transport equation depends on the smoothness of the solution (in angle only) and on the order of the filter. The results are confirmed by numerical experiments. Numerical tests have been implemented in MATLAB and are available online.