Monolithic projection-based method with staggered time discretization for solving non-Oberbeck–Boussinesq natural convection flows

Xiaomin Pan, Ki Ha Kim, Jung Il Choi

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Abstract

This paper presents an efficient monolithic projection-based method with staggered time discretization (MPM-STD) to examine the non-Oberbeck–Boussinesq (NOB) effects in several natural convection problems involving dramatic temperature-dependent changes in fluid properties. The proposed approach employs the Crank–Nicolson scheme along with staggered time discretization to discretize the momentum and energy equations. The momentum and energy equations are decoupled by evaluating the velocity vector at integral time levels (n+1), and the scalar variables (pressure and temperature) at half-integral time levels ([Formula presented]). The observed density variations in all terms result in a variable-coefficient Poisson equation, which is difficult to solve efficiently. The convergence is accelerated via adoption of an appropriate pressure-correction scheme that transforms the aforementioned Poisson equation to a constant-coefficient form. The numerical simulations concerning two-dimensional (2D) periodic NOB Rayleigh–Bénard convection (RBC) in glycerol and 2D differentially heated cavity (DHC) problem in air confirmed the second-order temporal and spatial accuracies of the proposed method. By simulating the 2D DHC problem in air and the RBC problem in liquid (water or glycerol) considering NOB effects, it is concluded that the proposed MPM-STD significantly mitigates the time-step restriction, thereby increasing the computational efficiency, which exceeds that of existing semi-implicit and explicit schemes. Moreover, the potential of the proposed approach with regard to solving challenging three-dimensional (3D) turbulent problems is demonstrated by performing direct simulations of turbulent RBCs under NOB effects involving temperature differences up to 60 K with a corresponding Rayleigh number (Ra=106).

Original languageEnglish
Article number111238
JournalJournal of Computational Physics
Volume463
DOIs
Publication statusPublished - 2022 Aug 15

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) (NRF-2017R1E1A1A0-3070161 and NRF-2022R1A2C2003643), the KISTI National Supercomputing Center with computing resources including technical support (KSC-2019-CHA-0009 and KSC-2020-CRE-0318), the Shanghai Sailing Program, China (20YF1413500), and by the National Natural Science Foundation of China (NO. 12101391).

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) ( NRF-2017R1E1A1A0-3070161 and NRF-2022R1A2C2003643 ), the KISTI National Supercomputing Center with computing resources including technical support ( KSC-2019-CHA-0009 and KSC-2020-CRE-0318 ), the Shanghai Sailing Program , China ( 20YF1413500 ), and by the National Natural Science Foundation of China (NO. 12101391 ).

Publisher Copyright:
© 2022 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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