Fully decoupled monolithic projection method for natural convection problems

Xiaomin Pan, Kyoungyoun Kim, Changhoon Lee, Jung Il Choi

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21 Citations (Scopus)


To solve time-dependent natural convection problems, we propose a fully decoupled monolithic projection method. The proposed method applies the Crank–Nicolson scheme in time and the second-order central finite difference in space. To obtain a non-iterative monolithic method from the fully discretized nonlinear system, we first adopt linearizations of the nonlinear convection terms and the general buoyancy term with incurring second-order errors in time. Approximate block lower-upper decompositions, along with an approximate factorization technique, are additionally employed to a global linearly coupled system, which leads to several decoupled subsystems, i.e., a fully decoupled monolithic procedure. We establish global error estimates to verify the second-order temporal accuracy of the proposed method for velocity, pressure, and temperature in terms of a discrete l2-norm. Moreover, according to the energy evolution, the proposed method is proved to be stable if the time step is less than or equal to a constant. In addition, we provide numerical simulations of two-dimensional Rayleigh–Bénard convection and periodic forced flow. The results demonstrate that the proposed method significantly mitigates the time step limitation, reduces the computational cost because only one Poisson equation is required to be solved, and preserves the second-order temporal accuracy for velocity, pressure, and temperature. Finally, the proposed method reasonably predicts a three-dimensional Rayleigh–Bénard convection for different Rayleigh numbers.

Original languageEnglish
Pages (from-to)582-606
Number of pages25
JournalJournal of Computational Physics
Publication statusPublished - 2017 Apr 1

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2014R1A2A1A11053140 and NRF-20151009350) and in part by the Yonsei University Future-leading Research Initiative of 2014.

Publisher Copyright:
© 2017 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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