Application of hp Adaptivity to the Multigroup Diffusion Equations
Application of hp Adaptivity to the Multigroup Diffusion Equations
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DOI：
10.13182/nse161-22
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发表时间：
2009-01
影响因子：
1.2
通讯作者：
Yaqi Wang;J. Ragusa
中科院分区：
文献类型：
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作者：
Yaqi Wang;J. Ragusa
摘要本文提出了一种应用于扩散方程的全自动hp网格加密策略。在惠普策略中，网格大小和多项式阶数都可以局部变化。数值结果表明，在均匀精化和h自适应策略下，对于所需未知数的一小部分，收敛速度是指数的。描述了在多群情况下的自适应处理和中子学计算中面向目标的估计器的推导。多基团分量的光滑度随能量基团的变化而变化很大；这一事实要求开发与基团相关的自适应空间网格。面向目标的过程将标准的惠普适应技术与基于伴随问题的同时解的面向目标的适应性相结合，以便计算感兴趣的量，例如子域中的反应速率和逐点的通量或电流。用这些算法对各种多组一维和二维扩散问题进行了测试，数值结果证实了理论预测的指数收敛速度。
Abstract This paper presents fully automated hp-mesh refinement strategies applied to diffusion equations. In hp strategies, both the mesh size and the polynomial order can vary locally. Numerical results show that exponential convergence rates are achieved for a fraction of the number of unknowns needed with uniform refinement and h-adaptive strategies. The treatment of adaptivity in the multigroup case and the derivation of goal-oriented estimators for neutronics calculations are described. The smoothness of the multigroup components can vary greatly as a function of the energy group; this fact called for the development of group-dependent adapted spatial meshes. The goal-oriented process combines the standard hp adaptation technique with a goal-oriented adaptivity based on the simultaneous solution of an adjoint problem in order to compute quantities of interest, such as reaction rates in subdomains and pointwise fluxes or currents. These algorithms are tested for various multigroup one-dimensional and two-dimensional diffusion problems, and the numerical results confirm the exponential convergence rates predicted theoretically.