|
|
二维柱坐标系中子输运问题的边界型算法
|
Abstract:
传统的确定论方法在研究高维度的中子输运方程时需要求解大型矩阵的逆矩阵，该过程将增加计算量、降低计算效率，因此本文采用了一种新型的边界型方法——半边界法(the Half Boundary Method)来解决此类问题。半边界方法利用已有的中子输运方程推导得出相邻两点之间的中子通量密度关系通式，然后迭代地应用此通式求出模型内部任一点与边界点之间的中子通量密度关系，即可得到整个模型的中子通量密度分布。半边界方法在已知一半边界条件处的中子通量密度即可求得模型内部任一点的中子通量密度，提高了计算效率。本文将半边界法在真空边界条件模型中得出的结果与NECP-MCX软件得到的数值结果进行比较，通过分析发现不同空间变量和角度变量离散数量对半边界法数值结果的影响，当空间变量M = 20，N = 40和角度变量H = 50，K = 32时，半边界法的平均误差为0.76%，具有较高精确度。
Traditional deterministic methods require solving the inverse matrix of large matrices when studying high-dimensional neutron transport equations, which increases computational complexity and reduces computational efficiency. Therefore, this paper adopts a new type of boundary type method—the Half Boundary Method to solve such problems. The half boundary method uses existing neutron transport equations to derive a general formula for the neutron flux density relationship between adjacent points, and then iteratively applies this formula to obtain the neutron flux density relationship between any point inside the model and the boundary point, thereby obtaining the neutron flux density distribution of the entire model. The half boundary method can obtain the neutron flux density at any point inside the model by knowing the neutron flux density at half of the boundary conditions, which improves computational efficiency. This article compares the results obtained by the half boundary method in the vacuum boundary condition model with the numerical results obtained by NECP-MCX software. Through analysis, it is found that the influence of different spatial and angular variables on the numerical results of the half-boundary method is significant. When the spatial variables M = 20, N = 40, and angular variables H = 50, K=32, the average error of the half boundary method is 0.76%, indicating high accuracy.
| [1] | 邓力, 袁国兴, 黄正丰, 等. 非定常粒子输运蒙特卡罗自适应并行计算[J]. 数值计算与计算机应用, 2003(2): 111-115. |
| [2] | Wareing, T.A., McGhee, J.M., Morel, J.E. and Pautz, S.D. (2001) Discontinuous Finite Element Sn Methods on Three-Dimensional Unstructured Grids. Nuclear Science and Engineering, 138, 256-268. https://doi.org/10.13182/nse138-256 |
| [3] | Markel, V. (2004) Modified Spherical Harmonics Method for Solving the Radiative Transport Equation. Waves in Random Media, 14, L13-L19. https://doi.org/10.1088/0959-7174/14/1/l02 |
| [4] | 卢皓亮, 吴宏春, 曹良志, 等. 非结构网格中子输运方程的离散纵标节块数值解法[J]. 西安交通大学学报, 2006(9): 1066-1069. |
| [5] | Coelho, P.J. (2001) The Role of Ray Effects and False Scattering on the Accuracy of the Standard and Modified Discrete Ordinates Methods. ICHMT Third International Symposium on Radiative Transfer, Antalya, 17-22 June 2001, 231-238. https://doi.org/10.1615/ichmt.2001.radiationsymp.90 |
| [6] | Tang, J., Huang, M., Yang, M., Zhao, Y. and Ouyang, X. (2018) A Procedure for Solving Transient Nonlinear Thermal Problems of High Burn-Up Nuclear Fuel Rods in a Light Water Reactor. Applied Thermal Engineering, 140, 455-465. https://doi.org/10.1016/j.applthermaleng.2018.04.134 |
| [7] | Huang, M., Tang, J., Zhao, Y. and Ouyang, X. (2017) A New Efficient and Accurate Procedure for Solving Heat Condution Problems. International Journal of Heat and Mass Transfer, 111, 508-519. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.109 |
| [8] | Zhao, Y., Huang, M., Tang, J., Ouyang, X. and Morita, C. (2019) A HBM Approach for Temperature and Heat Flux Convection-Diffusion Equations and Nonlinear Problems. Nuclear Engineering and Design, 342, 115-127. https://doi.org/10.1016/j.nucengdes.2018.11.023 |
| [9] | Tang, J., Huang, M., Zhao, Y., Maqsood, S. and Ouyang, X. (2018) Numerical Investigations on the Melting Process of the Nuclear Fuel Rod in Rias and Locas. International Journal of Heat and Mass Transfer, 124, 990-1002. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.001 |
| [10] | Tang, J., Huang, M., Zhao, Y., Ouyang, X. and Huang, J. (2017) A New Procedure for Solving Steady-State and Transient-State Nonlinear Radial Conduction Problems of Nuclear Fuel Rods. Annals of Nuclear Energy, 110, 492-500. https://doi.org/10.1016/j.anucene.2017.05.061 |
| [11] | Zhao, Y., Huang, M., Ouyang, X., Tang, J. and Morita, C. (2020) Half Boundary Method for Steady State Convection-Diffusion Equations with Different Boundary Conditions. Engineering Analysis with Boundary Elements, 113, 26-39. https://doi.org/10.1016/j.enganabound.2019.12.005 |
| [12] | 郑征, 吴宏春, 曹良志, 等. 一维平板几何中子输运方程P_N-DP_N耦合方法[J]. 核动力工程, 2010, 31(S2): 29-33. |
| [13] | 魏军侠, 袁光伟, 阳述林, 等. 二维柱几何非定常中子输运方程基于格式的界面预估校正并行算法[J]. 计算物理, 2012, 29(2): 198-204. |
| [14] | He, Q., Zheng, Q., Li, J., Wu, H., Shen, W., Cao, L., et al. (2021) NECP-MCX: A Hybrid Monte-Carlo-Deterministic Particle-Transport Code for the Simulation of Deep-Penetration Problems. Annals of Nuclear Energy, 151, Article 107978. https://doi.org/10.1016/j.anucene.2020.107978 |
