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.
© 2019 Elsevier Ltd
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes