JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (2): 109-117.doi: 10.6040/j.issn.1671-9352.0.2019.669

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Application of local non-intrusive reduced basis method in Rayleigh-Taylor instability

WEN Xiao1, LIU Qi2*, GAO Zhen2, DON Wai-sun2, LYU Xian-qing1   

  1. 1. Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao 266100, Shandong, China;
    2. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China
  • Published:2020-02-14

Abstract: A local non-intrusive reduced basis method(RBM)is proposed to simulate the evolution of Rayleigh-Taylor instability(RTI), in which the amplitude and time of initial small perturbations are considered as free parameters. RBM regards the solution as a linear combination of a set of reduced basis functions, which can be obtained by the proper orthogonal decomposition. Furthermore, the artificial neural network is used to establish the mapping relationship between the parameters and the coefficients of the reduced basis functions. Due to the structures of RTI becoming more and more complex with the increasing time, especially the rollup structures of small-scale vortices in the late stage, RTI is considered being divided into the early stage(linear)and the middle and late stage(quasi-non-linear and weak non-linear systems), i.e. time parameter is considered in stages. The time parameter is divided into three, five and six segments and the local RBM allows a potential speedup up to a factor of about four times faster than the global RBM with similar accuracy.

Key words: Rayleigh-Taylor instability, local non-intrusive reduced basis method, artificial neural network

CLC Number: 

  • O242
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