• Title/Summary/Keyword: Newton Iteration

Search Result 180, Processing Time 0.035 seconds

The JFNK method for the PWR's transient simulation considering neutronics, thermal hydraulics and mechanics

  • He, Qingming;Zhang, Yijun;Liu, Zhouyu;Cao, Liangzhi;Wu, Hongchun
    • Nuclear Engineering and Technology
    • /
    • v.52 no.2
    • /
    • pp.258-270
    • /
    • 2020
  • A new task of using the Jacobian-Free-Newton-Krylov (JFNK) method for the PWR core transient simulations involving neutronics, thermal hydraulics and mechanics is conducted. For the transient scenario of PWR, normally the Picard iteration of the coupled coarse-mesh nodal equations and parallel channel TH equations is performed to get the transient solution. In order to solve the coupled equations faster and more stable, the Newton Krylov (NK) method based on the explicit matrix was studied. However, the NK method is hard to be extended to the cases with more physics phenomenon coupled, thus the JFNK based iteration scheme is developed for the nodal method and parallel-channel TH method. The local gap conductance is sensitive to the gap width and will influence the temperature distribution in the fuel rod significantly. To further consider the local gap conductance during the transient scenario, a 1D mechanics model is coupled into the JFNK scheme to account for the fuel thermal expansion effect. To improve the efficiency, the physics-based precondition and scaling technique are developed for the JFNK iteration. Numerical tests show good convergence behavior of the iterations and demonstrate the influence of the fuel thermal expansion effect during the rod ejection problems.

Local Nonlinear Static Analysis via Static Condensation (강성응축기법을 이용한 국부 비선형 정적 해석)

  • Shin, Han-Seop;Oh, Min-Han;Boo, Seung-Hwan
    • Journal of the Korean Society of Marine Environment & Safety
    • /
    • v.27 no.1
    • /
    • pp.193-200
    • /
    • 2021
  • In this study, an analysis technique using static condensation is proposed for an efficient local nonlinear static analysis. The static condensation method is a model reduction method based on the degrees of freedom, and the analysis model is divided into a target part and a condensed part to be omitted. In this study, the nonlinear and linear parts were designated to the target and the omitted parts, respectively, and both the stiffness matrix and load vector corresponding to the linear part were condensed into the nonlinear part. After model condensation, the reduced model comprising the stiffness matrix and the load vector for the nonlinear part is constructed, and only this reduced model was updated through the Newton-Raphson iteration for an efficient nonlinear analysis. Finally, the efficiency and reliability of the proposed analysis technique were presented by applying it to various numerical examples.

NEWTON'S METHOD FOR SOLVING A QUADRATIC MATRIX EQUATION WITH SPECIAL COEFFICIENT MATRICES

  • Seo, Sang-Hyup;Seo, Jong-Hyun;Kim, Hyun-Min
    • Honam Mathematical Journal
    • /
    • v.35 no.3
    • /
    • pp.417-433
    • /
    • 2013
  • We consider the iterative solution of a quadratic matrix equation with special coefficient matrices which arises in the quasibirth and death problem. In this paper, we show that the elementwise minimal positive solvent of the quadratic matrix equations can be obtained using Newton's method if there exists a positive solvent and the convergence rate of the Newton iteration is quadratic if the Fr$\acute{e}$chet derivative at the elementwise minimal positive solvent is nonsingular. Although the Fr$\acute{e}$chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.

Numerical Solutions of Compressible Navier-Stokes Equations on Hybrid Meshes Using Newton-GMRES Method (Newton-GMRES 법을 사용한 혼합격자에서의 압축성 Navier-Stoke 방정식 수치 해석)

  • Choi Hwan-Seok
    • 한국전산유체공학회:학술대회논문집
    • /
    • 2000.05a
    • /
    • pp.178-183
    • /
    • 2000
  • An efficient Newton-GMRES algorithm is presented for computing two-dimensional steady compressible viscous flows on unstructured hybrid meshes. The scheme is designed on cell-centered finite volume method which accepts general polygonal meshes. Steady-state solution is obtained with pseudo-transient continuation strategy. The preconditioned, restarted general minimum residual(GMRES) method is employed in matrix-free form to solve the linear system arising at each Newton iteration. The incomplete LU fartorization is employed for the preconditioning of linear system. The Spalart-Allmars one equation turbulence model is fully coupled with the flow equations to simulate turbulence effect. The accuracy, efficiency and robustness of the presently developed method are demonstrated on various test problems including laminar and turbulent flows over flat plate and airfoils.

  • PDF

GLOBAL CONVERGENCE PROPERTIES OF THE MODIFIED BFGS METHOD ASSOCIATING WITH GENERAL LINE SEARCH MODEL

  • Liu, Jian-Guo;Guo, Qiang
    • Journal of applied mathematics & informatics
    • /
    • v.16 no.1_2
    • /
    • pp.195-205
    • /
    • 2004
  • To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

Fault Location Algorithm using Software Fault Tolerance (Software Fault Tolerance를 이용한 송전선로의 고장점 표정 알고리즘)

  • Jang, Yong-Won;Han, Seung-Su;Kim, Won-Ha
    • Proceedings of the KIEE Conference
    • /
    • 2003.11c
    • /
    • pp.875-877
    • /
    • 2003
  • This paper use fault location algorithm for single-phase-to-ground faults on the teed circuit of a parallel transmission line that use only local end voltage and current information. When Newton-Raphson iteration method is used, the Initial value may cause error or cause not suitable result. Suggested new calculation model uses NVP methodology, which is one of the fault tolerance technology to solve this problem. EMTP simulation result has shown effectiveness of the algorithm under various conditions.

  • PDF

Convergence Rate of Newton-Raphson Method (뉴톤-랩슨 반복법의 점근비율)

  • 이관제
    • The Korean Journal of Applied Statistics
    • /
    • v.6 no.2
    • /
    • pp.319-328
    • /
    • 1993
  • The actual convergence rate of Newton-Raphson iteration method at each step is studied under the regularity conditions for the limiting distribution: The convergence rate of it is accelerated with good starting values. Hence we can decide a number of iterations according to our purposes.

  • PDF

NUMERICAL METHODS SOLVING THE SEMI-EXPLICIT DIFFERENTIAL-ALGEBRAIC EQUATIONS BY IMPLICIT MULTISTEP FIXED STEP SIZE METHODS

  • Kulikov, G.Yu.
    • Journal of applied mathematics & informatics
    • /
    • v.4 no.2
    • /
    • pp.341-378
    • /
    • 1997
  • We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

Jacobian-free Newton Krylov two-node coarse mesh finite difference based on nodal expansion method

  • Zhou, Xiafeng
    • Nuclear Engineering and Technology
    • /
    • v.54 no.8
    • /
    • pp.3059-3072
    • /
    • 2022
  • A Jacobian-Free Newton Krylov Two-Nodal Coarse Mesh Finite Difference algorithm based on Nodal Expansion Method (NEM_TNCMFD_JFNK) is successfully developed and proposed to solve the three-dimensional (3D) and multi-group reactor physics models. In the NEM_TNCMFD_JFNK method, the efficient JFNK method with the Modified Incomplete LU (MILU) preconditioner is integrated and applied into the discrete systems of the NEM-based two-node CMFD method by constructing the residual functions of only the nodal average fluxes and the eigenvalue. All the nonlinear corrective nodal coupling coefficients are updated on the basis of two-nodal NEM formulation including the discontinuity factor in every few newton steps. All the expansion coefficients and interface currents of the two-node NEM need not be chosen as the solution variables to evaluate the residual functions of the NEM_TNCMFD_JFNK method, therefore, the NEM_TNCMFD_JFNK method can greatly reduce the number of solution variables and the computational cost compared with the JFNK based on the conventional NEM. Finally the NEM_TNCMFD_JFNK code is developed and then analyzed by simulating the representative PWR MOX/UO2 core benchmark, the popular NEACRP 3D core benchmark and the complicated full-core pin-by-pin homogenous core model. Numerical solutions show that the proposed NEM_TNCMFD_JFNK method with the MILU preconditioner has the good numerical accuracy and can obtain higher computational efficiency than the NEM-based two-node CMFD algorithm with the power method in the outer iteration and the Krylov method using the MILU preconditioner in the inner iteration, which indicates the NEM_TNCMFD_JFNK method can serve as a potential and efficient numerical tool for reactor neutron diffusion analysis module in the JFNK-based multiphysics coupling application.