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

Fingerprint

Natural convection
free convection
projection
convection
integers
Poisson equation
Momentum
Boundary conditions
Rayleigh number
pressure distribution
preserving
Convection
Computer simulation
temperature distribution
velocity distribution
grids
boundary conditions
momentum
predictions
Temperature

All Science Journal Classification (ASJC) codes

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

Cite this

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title = "Efficient monolithic projection method with staggered time discretization for natural convection problems",
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–B{\'e}nard 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–B{\'e}nard convection under different thermal boundary conditions for a Rayleigh number up to 1010, three-dimensional turbulent Rayleigh–B{\'e}nard convection in the range of 1×105–2×107 in horizontal periodic domain, and three-dimensional turbulent Rayleigh–B{\'e}nard 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.",
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Efficient monolithic projection method with staggered time discretization for natural convection problems. / Pan, Xiaomin; Kim, Ki Ha; Choi, Jung Il.

In: International Journal of Heat and Mass Transfer, Vol. 144, 118677, 12.2019.

Research output: Contribution to journalArticle

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