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: 压水堆堆芯热工水力计算需要求解多变量强耦合的微分方程组,由于不同子通道的各个物理量之间耦合关系复杂,离散后得到的代数方程组求解困难,常见的迭代求解方法经常不收敛或数值不稳定。针对此问题,本文通过对系数矩阵分块结构的分析,根据系数矩阵不同物理量的稀疏结构,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: Thermal-hydraulic simulations of pressurized water reactor cores involve solving complex, multi-variable differential equation systems with strong couplings. Owing to the intricate interactions among various physical quantities across different sub-channels, it is challenging to solve the resulting algebraic equation systems after discretization. Traditional iterative techniques frequently encounter convergence difficulties or exhibit numerical instability. To tackle this challenge, this study investigates the block structure of the coefficient matrix and leverages the sparse distribution of different physical quantities within it. 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 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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