Coupled Space-Angle Adaptivity for Radiation Transport Calculations
Coupled Space-Angle Adaptivity for Radiation Transport Calculations
复制标题
用于辐射传输计算的耦合空间角度自适应性
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
C. D. de Oliveira
中科院分区：
文献类型：
--
作者：
HyeongKae Park;C. D. de Oliveira
摘要基于变分有限元-球谐法（FE-PN）离散输运方程的二阶偶奇偶形式，提出了一种耦合空间角后验误差分析和自适应辐射输运计算方法。利用对偶性参数导出了偶宇称角通量中全局L2范数的严格后验误差估计。该自适应算法首先在空间变量上寻求收敛，然后将空间收敛解投影到高阶PN方程上估计角截断误差，从而获得空间离散化和角离散化的独立误差分量。通过对一维和二维代表性问题的误差指标与真实误差的比较，评价了所提出的耦合空间角自适应细化策略的有效性。采用制造溶液法和替代输送溶液法来提供真实误差。对比表明，空间角自适应框架能够引导FE-PN方法逼近真解。
Abstract This paper describes the development of a coupled space-angle a posteriori error analysis and adaptive method for radiation transport calculations based on the second-order, even-parity form of the transport equation discretized by a variational finite element–spherical harmonics method (FE-PN). Rigorous a posteriori error estimates for the global L2 norm in the even-parity angular flux are derived by utilizing duality arguments. Separate error components for the spatial and angular discretizations are obtained by the adaptive algorithm by first seeking convergence in the spatial variable and then by projecting the spatially converged solution onto the higher-order PN equation to estimate the angular truncation error. The validity of the developed coupled space-angle adaptive refinement strategy is assessed by comparing the developed error indicator with the true error for representative problems in one and two dimensions. The method of manufactured solutions and alternative transport solution methods are used to provide the true error. Comparisons indicate that the space-angle adaptivity framework is capable of guiding the FE-PN method toward the true solution.