A Newton-Krylov method with dense row decomposition for steady-state neutronics/thermal-hydraulics problems. (May 2022) - Liu, Baokun; Wu, Yingjie; Zhang, Han; Guo, Jiong; Li, Fu
Abstract: Steady-state neutronics/thermal-hydraulics simulation is a typical and important issue for nuclear design and analysis. Newton-Krylov method is a promising choice for solving the multi-physics nonlinear coupling issue due to its high convergence rate. In practice, how to compute Jacobian matrix efficiently and automatically is a challenging topic for Newton-Krylov method. Graph coloring is an effective technology which utilizes the sparse structure of Jacobian matrix. However, the efficiency of graph coloring method suffers from local dense row in Jacobian matrix due to the lack of sparse structure, such as the steady-state neutronics/thermal-hydraulics problem. In this work, a dense row decomposition method based on variable substitution is proposed to make up the defect of graph coloring method by eliminating the dense row. A steady-state multi-physics coupling problem is conducted to demonstrate the performance of the proposed method. The dense row decomposition method can significantly reduce computational cost, and a speedup ratio of over 10 is achieved compared with traditional methods.