求解热工子通道问题的场分裂预处理方法

Field-Split Preconditioner for Solving Thermal-Hydraulic Sub-channel Problems

  • 摘要: 针对压水堆堆芯热工水力多变量强耦合的微分方程组离散求解,本文通过对系数矩阵分块结构进行分析,根据系数矩阵不同物理量的稀疏结构、不同子通道之间物理量的耦合关系,以及变量的排列顺序,借助对称乘性场分裂方法进行解耦,将大型耦合方程组按物理场拆分为3个子系统分别求解,建立了基于对称乘性场分裂的预处理方法。基于4个具有不同通道规模的典型工况进行数值试验,相比对整个代数系统直接使用代数多重网格(AMG)或不完全LU分解(ILU)的传统预处理方法,本文的预处理方法能够有效提高Krylov子空间迭代的收敛速度和求解精度。

     

    Abstract: For the discretized solution of the multivariable strongly coupled differential equations in pressurized water reactor core thermal-hydraulic analysis, this study analyzes the block structure of the coefficient matrix. By considering the sparse distribution of different physical quantities, the coupling relationships among variables across different sub-channels, and the ordering of variables, the system is decoupled using a symmetric multiplicative field-split approach. By employing a symmetric multiplicative field-split approach, the system is decoupled. The extensive coupled equations are broken down into three subsystems based on physical fields for independent resolution. Additionally, a preconditioning strategy rooted in symmetric multiplicative field-split is developed. Numerical evaluations were performed under four representative operational scenarios with varying channel scales. In comparison to traditional preconditioning approaches that directly apply Algebraic Multigrid (AMG) or Incomplete LU (ILU) factorization to the entire algebraic system, the proposed method significantly enhances the convergence rate and solution precision of Krylov subspace iterations.

     

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