Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Preconditioned Jacobian-free Newton-Krylov fully implicit high order WENO schemes and flux limiter methods for two-phase flow models

  • Zhou, Xiafeng (Department of Nuclear Engineering and Technology, School of Energy and Power Engineering, Huazhong University of Science and Technology) ;
  • Zhong, Changming (Department of Nuclear Engineering and Technology, School of Energy and Power Engineering, Huazhong University of Science and Technology) ;
  • Li, Zhongchun (Nuclear Power Institute of China) ;
  • Li, Fu (Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Institute of Nuclear and New Energy Technology, Tsinghua University)
  • Received : 2020.10.26
  • Accepted : 2021.07.16
  • Published : 2022.01.25
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Abstract

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.

Keywords

Acknowledgement

This research is supported by the National Natural Science Foundation of China (12005073),the Project of Nuclear Power Technology Innovation Center of Science Technology and Industry for National Defense (HDLCXZX-2021-HD-033, HDLCXZX-2019-ZH-26), Science and Technology on Reactor System Design Technology Laboratory Foundation Project (HT-KFKT-10-2018005).

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