For a more efficient algorithm, we introduce staggered time discretization to improve the previous method (Pan et al., 2017), fully decoupled monolithic projection method with one Poisson equation (FDMPM-1P), to solve time-dependent natural convection problems. The momentum and energy equations are discretized using the Crank–Nicolson scheme at the staggered time grids, in which temperature and pressure fields are evaluated at half-integer time levels (n+ [Formula presented] ), while the velocity fields are evaluated at integer time levels (n+1). Numerical simulations of two-dimensional (2D) Rayleigh–Bénard convection show that the proposed method is more computationally efficient and stable than FDMPM-1P, while preserving the second-order spatial and temporal accuracy. Further, the proposed method provides accurate predictions of 2D Rayleigh–Bénard convection under different thermal boundary conditions for a Rayleigh number up to 1010, three-dimensional turbulent Rayleigh–Bénard convection in the range of 1×105–2×107 in horizontal periodic domain, and three-dimensional turbulent Rayleigh–Bénard convection in the range of 1×106–1×107 in bounded domain. Finally, we theoretically confirmed that the proposed method is second-order in time and it is more stable than FDMPM-1P for small Ra.
|Journal||International Journal of Heat and Mass Transfer|
|Publication status||Published - 2019 Dec|
Bibliographical noteFunding Information:
This work was supported by National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science and ICT) (No. NRF-20151009350) and KISTI (K-18-L12-C08), and in part by Yonsei University (Yonsei Frontier Lab.?Young Researcher Supporting Program) of 2018.
This work was supported by National Research Foundation of Korea (NRF) grant funded by the Korean government ( Ministry of Science and ICT ) (No. NRF-20151009350 ) and KISTI ( K-18-L12-C08 ), and in part by Yonsei University (Yonsei Frontier Lab.–Young Researcher Supporting Program) of 2018.
© 2019 Elsevier Ltd
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes