Efficient monolithic projection method with staggered time discretization for natural convection problems

Xiaomin Pan, Ki Ha Kim, Jung Il Choi

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number118677
JournalInternational Journal of Heat and Mass Transfer
Volume144
DOIs
Publication statusPublished - 2019 Dec

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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