Multigrid Newton-Krylov method for radiation in diffusive semitransparent media
Multigrid Newton-Krylov method for radiation in diffusive semitransparent media
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漫射半透明介质辐射的多重网格牛顿-克雷洛夫方法
DOI：
10.1016/j.cam.2006.04.016
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发表时间：
2007
影响因子：
2.4
通讯作者：
M. Seaid
中科院分区：
文献类型：
--
作者：
M. Seaid
提出了一种快速多重网格算法，用于非灰透明介质中扩散辐射的简化PN（SPN）近似。该方法包括重新制定的方程作为一个非线性不动点问题的温度。给定一个网格层次，时间和空间离散分别使用二阶隐式和有限差分法。在每个网格级别，牛顿-克雷洛夫算法应用于离散方程。作为粗糙网格上的平滑器，我们提出了Atkinson-Brakhage算子。数值结果显示，玻璃冷却过程中使用不同的几何外壳。SPN近似捕捉正确的渐近行为的数值解的计算成本低于使用完整的辐射传输方程。
We present a fast multigrid solver for simplified PN(SPN) approximations to the diffusive radiation in non-grey semitransparent media. The method consists on reformulating the equations as a nonlinear fixed point problem in the temperature only. Given a mesh hierarchy, time and space discretizations are performed using second-order implicit and finite differencing methods, respectively. At each mesh level, a Newton–Krylov algorithm is applied to the discrete equations. As a smoother on the coarse meshes we propose the Atkinson–Brakhage operator. Numerical results are shown for glass cooling process using different geometry enclosures. The SPNapproximations capture the correct asymptotic behavior of the numerical solution with a computational cost lower than using the full radiative transfer equations.