Jacobian-free Newton-Krylov Method For Two-phase Flow Models And Neutron Physics Model With Thermal-hydraulic Feedback

The reactor is a large,complex multi-physics coupling system consisting of multiple interacting physical fields.Solving the two-phase flow model and the neutron physics model with thermal-hydraulic feedback are the cores of the reactor coupled calculation analysis.Up to now,the operator splitting iteration method has been employed in most reactor calculation analysis codes.However,the operator splitting iteration method can’t ensure convergence and calculation efficiency.In order to ensure the convergence and efficiency of the reactor systems,the Jacobian-Free Newton Krylov(JFNK)framework is investigated and established.A JFNK multiphysics environment COME＿JFNK is developed to help to create multiphysics simulation codes which are based on reactor calculation analysis models.In addition,the two-phase flow models and neutronics /thermal-hydraulics coupling model are created with COME＿JFNK.Firstly,this thesis carries out a detailed theoretical analysis of the JFNK method and then extracts the critical problems to be solved when applying the JFNK method to a multiphysics coupling environment.A mathematical preprocessing acceleration method based on finite-difference is established as the preprocessing of the JFNK method.The idea of constructing the residual equation with physical preconditioning methods by combining the JFNK method is analyzed.As a result,based on the JFNK framework,a multi-physics environment,COME＿JFNK,is established,which applies in practical engineering reactor calculation codes.And then,based on COME＿JFNK,the preconditioned JFNK fully implicit high-order WENO and FL schemes are proposed to solve the transient two-phase two-fluid models.After that,WENO＿JFNK and FL＿JFNK are developed,and then their convergence,computational cost,and efficiency are analyzed detailedly by testing some two-phase problems.Numerical results show that WENO＿JFNK and FL＿JFNK can significantly reduce numerical diffusion,but WENO＿JFNK gives stabler and more accurate solutions for the tested problems.In general,the proposed acceleration methods can significantly improve convergence speed and efficiency.Lastly,the neutron nodal method is integrated into the multiphysics environment COME＿JFNK.As a result,the multiphysics simulation code was successfully developed for neutronics/thermal-hydraulics coupled problems.Additionally,the physical preconditioning methods and forcing term in the inexact Newton method are developed,which can effectively improve the efficiency of the Krylov method and the convergence property of Newton’s iterative steps.Numerical results show that the coupled code COME＿JFNK has higher efficiency and a faster convergence rate than the original neutron nodal method.