核事故污染物大气扩散的三维近实时模拟方法研究
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摘要
当核电站发生放射性物质泄漏事故时,及时地预报污染物的分布和浓度将为制定应急预案提供重要的技术支撑。求解污染物在大气中运输和扩散模拟时,虽边界条件、源项及其他物理参数可能会发生变化,但控制方程的数学形式不变。本文采用了缩减基有限元方法将这些变化的条件视为参数,利用少数具有代表性的经典有限元解构造了解空间的基函数,最后采用了仿射分解将系统拆分为参数有关部分和参数无关部分,大幅降低了系统矩阵和载荷向量的组装难度。实验结果表明,在线阶段的求解速度提高3个数量级左右,因此该方法可用于污染物扩散的近实时模拟。
When a radioactive material leakage accident occurs in a nuclear power plant, the timely forecast of the distribution and concentration of pollutant will provide important technical support for the formulation of emergency plan. While solving the transport and diffusion simulation of pollutant in the atmosphere, the boundary conditions, source terms and other physical parameters may change, but the mathematical form of the control equation is constant. The reduced basis finite element method was used to regard these changing conditions as parameters, and the basis functions of solution space were constructed by using a few representative classical finite element solutions. The system was divided into parameter-related part and parameter-independent part by affine decomposition, which greatly reduced the difficulty of assembling system matrix and load vector. The experimental results show that the solution speed of the online stage is increased by about three orders of magnitude. Therefore, this method can be applied to near real-time simulation of pollutant diffusion.
When a radioactive material leakage accident occurs in a nuclear power plant, the timely forecast of the distribution and concentration of pollutant will provide important technical support for the formulation of emergency plan. While solving the transport and diffusion simulation of pollutant in the atmosphere, the boundary conditions, source terms and other physical parameters may change, but the mathematical form of the control equation is constant. The reduced basis finite element method was used to regard these changing conditions as parameters, and the basis functions of solution space were constructed by using a few representative classical finite element solutions. The system was divided into parameter-related part and parameter-independent part by affine decomposition, which greatly reduced the difficulty of assembling system matrix and load vector. The experimental results show that the solution speed of the online stage is increased by about three orders of magnitude. Therefore, this method can be applied to near real-time simulation of pollutant diffusion.
引文
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[2] 肖明明. 核电厂核事故放射性污染物扩散模拟研究[D]. 沈阳:辽宁大学,2015.
[3] 余琦,刘原中. 分段烟羽模型和烟团模型在核事故应急中的应用比较[J]. 核科学与工程,2001,21(3):288-292. YU Qi, LIU Yuanzhong. Application of a Gaussian segmented plume model and a Lagrangian puff model during the nuclear emergency[J]. Chinese Journal of Nuclear Science and Engineering, 2001, 21(3): 288-292(in Chinese).
[4] 李云云. 高斯烟羽模型的改进及在危化品泄漏事故模拟中的应用[D]. 广州:广州大学,2013.
[5] 张纯禹,陈恭,王一正,等. 快速求解参数化偏微分方程的缩减基有限元方法及其在核工程中的应用[J]. 计算数学,2017,39(4):431-444. ZHANG Chunyu, CHEN Gong, WANG Yi-zheng, et al. Fast solution of parametrized partial differential equations by using reduced basis finite element method[J]. Mathematica Numerica Sinica, 2017, 39(4): 431-444(in Chinese).
[6] 利伯斯坦H M. 偏微分方程理论[M]. 北京:高等教育出版社,1983.
[7] 马营利,雷飞,孙军,等. 基于部分参数显式化格式的缩减基快速计算方法及应用[J]. 机械科学与技术,2013,32(7):968-972. MA Yingli, LEI Fei, SUN Jun, et al. A rapid computation method of reduced basis based on partial explicit parameterized formulation and its application[J]. Mechanical Science and Technology for Aerospace Engineering, 2013, 32(7): 968-972(in Chinese).
[8] 冯浩然. 大气风场中排放物的迁移、扩散与分布特性研究[D]. 南京:东南大学,2013.
[9] 蔡树棠,刘宇陆. 湍流理论[M]. 上海:上海交通大学出版社,1993.
[10] SHOWALTER R E. Hilbert space methods for partial differential equations[J]. Electronic Journal of Differential Equations, 1979, 121(2): 261-270.
[11] 李社环,朱起定. Lax-Milgram定理的进一步推广及其应用[J]. 高等学校计算数学学报,1992(2):169-178. LI Shehuan, ZHU Qiding. The further generalization of the Lax-Milgram theorem and its applications[J]. Numerical Mathematics: A Journal of Chinese Universities, 1992(2): 169-178(in Chinese).
[12] 李荣华. 边值问题的Galerkin有限元法[M]. 北京:科学出版社,2005.
[13] HESTHAVEN J S, ROZZA G, STAMM B. Certified reduced basis methods for parametrized partial differential equations[M]. France: Springer International Publishing, 2016.