Equivalent low-order angular flux nonlinear finite difference equation of MOC transport calculation
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Equivalent low-order angular flux nonlinear finite difference equation of MOC transport calculation Li-Xun Liu1,2
•
Chen Hao1 • Yun-Lin Xu3
Received: 24 July 2020 / Revised: 13 October 2020 / Accepted: 16 October 2020 Ó China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society and Springer Nature Singapore Pte Ltd. 2020
Abstract The key issue in accelerating method of characteristics (MOC) transport calculations is in obtaining a completely equivalent low-order neutron transport or diffusion equation. Herein, an equivalent low-order angular flux nonlinear finite difference equation is proposed for MOC transport calculations. This method comprises three essential features: (1) the even parity discrete ordinates method is used to build a low-order angular flux nonlinear finite difference equation, and different boundary condition treatments are proposed; (2) two new defined factors, i.e., the even parity discontinuity factor and odd parity discontinuity factor, are strictly defined to achieve equivalence between the low-order angular flux nonlinear finite difference method and MOC transport calculation; (3) the energy group and angle are decoupled to construct a symmetric linear system that is much easier to solve. The equivalence of this low-order angular flux nonlinear finite difference equation is analyzed for two-dimensional (2D) pin, 2D assembly, and 2D C5G7 benchmark problems. Numerical results demonstrate that a low-order angular flux nonlinear finite difference equation that is completely
This work was supported by the National Key R&D Program of China (No. 2018YFE0180900). & Chen Hao [email protected] 1
Fundamental Science On Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin 150001, China
2
Institute of Nuclear and New Energy Technology (INET), Tsinghua University, Beijing 100084, China
3
Purdue University, West Lafayette, IN 47907, USA
equivalent to the pin-resolved transport equation is established. Keywords Angular flux Equivalence Even parity discrete ordinates method Nonlinear finite difference
1 Introduction Significant advances in high-performance computing clusters (HPCs) have enabled three-dimensional (3D) whole-core high-fidelity heterogeneous transport simulations at the subpin level. This is becoming increasingly important for improving the reactor performance and safety as well as providing an efficient tool for more complex and novel designs. A numerical simulation method for solving the neutron transport equation, i.e., the method of characteristics (MOC), has garnered significant attention in whole-core high-fidelity simulations as the MOC can be applied to obtain detailed flux distributions without any restrictions on the geometry mesh. Hence, efficient performances can be achieved on various HPC systems. In fact, many famous high-fidelity neutron transport simulation codes were developed based o
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