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RISS 인기검색어
- 검색키워드
- 저자 : Xiafeng Zhou (검색결과 4 건)
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Delta-form-based method of solving high order spatial discretization schemes for neutron transport
Zhou, Xiafeng,Zhong, Changming,Li, Fu Korean Nuclear Society 2021 Nuclear Engineering and Technology Vol.53 No.7
Delta-form-based methods for solving high order spatial discretization schemes are introduced into the reactor S<sub>N</sub> transport equation. Due to the nature of the delta-form, the final numerical accuracy only depends on the residuals on the right side of the discrete equations and have nothing to do with the parts on the left side. Therefore, various high order spatial discretization methods can be easily adopted for only the transport term on the right side of the discrete equations. Then the simplest step or other robust schemes can be adopted to discretize the increment on the left hand side to ensure the good iterative convergence. The delta-form framework makes the sweeping and iterative strategies of various high order spatial discretization methods be completely the same with those of the traditional S<sub>N</sub> codes, only by adding the residuals into the source terms. In this paper, the flux limiter method and weighted essentially non-oscillatory scheme are used for the verification purpose to only show the advantages of the introduction of delta-form-based solving methods and other high order spatial discretization methods can be also easily extended to solve the S<sub>N</sub> transport equations. Numerical solutions indicate the correctness and effectiveness of delta-form-based solving method.
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Jacobian-free Newton Krylov two-node coarse mesh finite difference based on nodal expansion method
Zhou Xiafeng 한국원자력학회 2022 Nuclear Engineering and Technology Vol.54 No.8
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 threedimensional (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
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Xiafeng Zhou,Changming Zhong,Zhongchun Li,Fu Li 한국원자력학회 2022 Nuclear Engineering and Technology Vol.54 No.1
Motivated by the high-resolution properties of high-order Weighted Essentially Non-Oscillatory (WENO) and flux limiter (FL) for steep-gradient problems and the robust convergence of Jacobian-free Newton-Krylov (JFNK) methods for nonlinear systems, the preconditioned JFNK fully implicit high-order WENO and FL schemes are proposed to solve the transient two-phase two-fluid models. Specially, the second-order fully-implicit BDF2 is used for the temporal operator and then the third-order WENO schemes and various flux limiters can be adopted to discrete the spatial operator. For the sake of the generalization of the finite-difference-based preconditioning acceleration methods and the excellent convergence to solve the complicated and various operational conditions, the random vector instead of the initial condition is skillfully chosen as the solving variables to obtain better sparsity pattern or more positions of non-zero elements in this paper. Finally, the WENO_JFNK and FL_JFNK codes are developed and then the two-phase steep-gradient problem, phase appearance/disappearance problem, U-tube problem and linear advection problem are tested to analyze the convergence, computational cost and efficiency in detailed. Numerical results show that WENO_JFNK and FL_JFNK can significantly reduce numerical diffusion and obtain better solutions than traditional methods. WENO_JFNK gives more stable and accurate solutions than FL_JFNK for the test problems and the proposed finite-difference-based preconditioning acceleration methods based on the random vector can significantly improve the convergence speed and efficiency.
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Dong Shichang,Zhou Xiafeng,Yang Jun 한국원자력학회 2020 Nuclear Engineering and Technology Vol.52 No.7
Filtered containment venting system (FCVS) is one of the severe accident mitigation systems designed to release containment pressurization to maintain its integrity. The thermal-hydraulic behaviors in FCVSs are important since they affect the operation characteristics of the FCVS. In this study, a representative FCVS was modeled by RELAP5/Mod3.3 code, and the Station BlackOut (SBO) was chosen as an accident scenario. The thermal-hydraulic behaviors of an FCVS during long-term operation with two venting strategies (open-and-close strategy, open-and-non-close strategy) and the sensitivity analysis of important parameters were investigated. The results show that the FCVS can operate up to 250 h with a periodic open-and-close strategy during an SBO. Under the combined effects of steam condensation and water evaporation, the solution inventory in the FCVS increases during the venting phase and decreases during the intermission phase, showing a periodic pattern. Under this condition, the appropriate initial water level is 3e4 m; however, it should be adjusted according to the environment temperature. The FCVS can accommodate a decay heat power of 150e260 kW and may need to feed water for a higher decay heat power or drain water for a lower decay heat power during the late phase. The FCVS can function within an opening pressure range from 450 kPa to 500 kPa and a closing pressure range between 250 kPa and 350 kPa. When the open-and-non-close strategy is adopted, the solution inventory increases quickly in the early venting phase due to steam condensation and then decreases gradually due to the evaporation of water; drying-up may occur in the late venting phase. Decreasing the venting pipe diameter and increasing the initial water level can mitigate the evaporation of the scrubbing solution. These results are expected to provide useful references for the design and engineering application of FCVSs
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