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利用Jacobian-free Newton-Krylov(JFNK)方法联立求解中子-热工耦合问题,采用非线性预处理方式,以避免求解非线性残差,使得JFNK具有可以充分利用原有的中子-热工计算程序,易于实现“黑箱”耦合的特点。对非线性预处理的相关性质进行分析,同时对非线性预处理与线性预处理的区别与联系以及计算效率进行理论分析。以二维简化中子-热工耦合模型作为算例,对比非线性预处理/线性预处理JFNK方法、传统耦合求解方法的计算效率。结果表明:非线性预处理/线性预处理JFNK方法的计算效率比传统方法具有明显优势,线性预处理的计算效率高于非线性预处理。
Solving the neutron-thermal coupling problem by using the Jacobian-free Newton-Krylov (JFNK) method, a nonlinear preconditioning method is adopted to avoid solving the nonlinear residual, making JFNK have the advantages of fully utilizing the existing neutron-heat Engineering calculation program, easy to implement “black box ” coupling characteristics. The related properties of nonlinear preprocessing are analyzed. At the same time, the differences and relations between nonlinear preprocessing and linear preprocessing and the computational efficiency are analyzed theoretically. Taking the two-dimensional simplified neutron-thermal coupling model as an example, the computational efficiency of the traditional coupled solution method is compared with the nonlinear preconditioning / linear preconditioning JFNK method. The results show that the computational efficiency of the nonlinear preconditioning / linear preconditioning JFNK method is obviously superior to that of the traditional method. The computational efficiency of linear preconditioning is higher than that of nonlinear preconditioning.