基于有限差分Newton-Krylov方法的中子-热工联立求解

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Simultaneous Solution of Neutron/Thermal-Hydraulic Coupled System Based on Finite Difference Newton-Krylov Method

Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing, 100084, China

摘要: 利用Newton-Krylov方法联立求解中子-热工耦合问题,Newton迭代具有收敛速度高于传统耦合方法的优势。采用有限差分方法构建Jacobian矩阵,以避免需要Jacobian矩阵的解析表达式。利用有限差分方法直接计算Jacobian矩阵存在计算代价过大的缺点,通过考虑Jacobian矩阵的稀疏结构,减少了Jacobian矩阵的计算代价。通过二维简化中子-热工耦合模型,给出了Newton-Krylov方法与传统耦合方法的计算效率的对比,Newton-Krylov方法的计算效率具有明显优势。
- 中子-热工耦合 /
- Newton-Krylov方法 /
- 稀疏Jacobain矩阵 /
- 有限差分近似
Abstract: The Newton-Krylov method is utilized to solve the Neutron/Thermal-Hydraulic coupled system in nuclear reactors which convergence rate is higher than the traditional method. Finite difference method is employed to calculate the Jacobian matrix to avoid the analytical expressions of Jacobian matrix. The sparse pattern of the Jacobian matrix is considered to build a higher efficient algorithm compared with the dense Jacobian matrix. The numerical result shows that the advanced Newton-Krylov method is more efficient than the traditional method for the simplified reactor model.
- Neutronic/Thermal-hydraulic coupled /
- Newton-Krylov method /
- Sparse Jacobain matrix /
- Finite difference approximation