Spectral Element Method with Adaptive Artificial Diffusion for Solving the Radiative Transfer Equation
Spectral Element Method with Adaptive Artificial Diffusion for Solving the Radiative Transfer Equation
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DOI：
10.1080/10407790802035117
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
J. M. Zhao;L. H. Liu
中科院分区：
文献类型：
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作者：
J. M. Zhao;L. H. Liu
为解决辐射传输问题中的射线效应，提出了一种自适应各向同性人工扩散（AISO）谱元方法。通过考虑射线效应和伪散射的耦合方式，从局部角度离散尺度和局部空间离散尺度两个方面解析地确定了人工扩散系数。该方案是容易和有效地实现下的谱或有限元方法的框架。研究和比较了各种人工扩散方案的性能。流向人工扩散方案只负责稳定强对流引起的不稳定性，而各向同性人工扩散方案在减轻“摆动”在低阶和高阶空间近似表现出非常好的性能。数值实验表明，采用AISO格式的谱元方法是稳定的、高精度的，能够有效地求解简单和复杂几何条件下的辐射传输问题，并能有效地消除各种射线的影响.
An adaptive isotropically artificial diffusion (AISO) scheme is developed for the spectral element method to mitigate the ray effects encountered in the solution of radiative transfer problems. By considering the coupled manner of ray effects and false scattering, the artificial diffusion coefficient is determined heuristically from both local angular discretization scale and local spatial discretization scale. The scheme is easily and efficiently implemented under the spectral or finite-element method framework. The performance of various artificial diffusion schemes is studied and compared. The streamwise artificial diffusion schemes are only responsible for stabilization of strong convection-induced instability, while the isotropically artificial diffusion scheme shows very good performance in mitigating the “wiggles” in both low- and high-order spatial approximation. Numerical experiments show that the spectral element method with the AISO scheme is stable, high-order-accurate, and effective for solving radiative transfer in simple and complex geometries, and also robust for mitigating ray effects of various origins.