Temporal, spatial and thermal features of 3-D Rayleigh-Bénard convection by a least-squares finite element method

Li Q. Tang; Tate T.H. Tsang

doi:10.1016/S0045-7825(96)01053-5

Temporal, spatial and thermal features of 3-D Rayleigh-Bénard convection by a least-squares finite element method

Li Q. Tang, Tate T.H. Tsang

Chemical and Materials Engineering

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

Numerical solutions of 3-D time-dependent Rayleigh-Bénard convection are presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh numbers Ra = 8 × 10³, 2.4 × 10⁴ and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, 'T-shaped' rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.

Original language	English
Pages (from-to)	201-219
Number of pages	19
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	140
Issue number	3-4
DOIs	https://doi.org/10.1016/S0045-7825(96)01053-5
State	Published - Jan 30 1997

Bibliographical note

Funding Information:
The work was partially supportedb y the National ScienceF oundation (NSF/KY EPSCoR program) and the Center for Computational Sciences at the University of Kentucky. TTT is also partially supported by a grant from the U.S. Environmental Protection Agency. The authors appreciatet he reviewerst horough and thoughtfulc ommentsa nd suggestionsw hich helped us to improve this paper.

Funding

The work was partially supportedb y the National ScienceF oundation (NSF/KY EPSCoR program) and the Center for Computational Sciences at the University of Kentucky. TTT is also partially supported by a grant from the U.S. Environmental Protection Agency. The authors appreciatet he reviewerst horough and thoughtfulc ommentsa nd suggestionsw hich helped us to improve this paper.

Funders	Funder number
Center for Computational Sciences
National Science Foundation (NSF)
U.S. Environmental Protection Agency

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/S0045-7825(96)01053-5

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title = "Temporal, spatial and thermal features of 3-D Rayleigh-B{\'e}nard convection by a least-squares finite element method",

abstract = "Numerical solutions of 3-D time-dependent Rayleigh-B{\'e}nard convection are presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh numbers Ra = 8 × 103, 2.4 × 104 and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, 'T-shaped' rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.",

author = "Tang, {Li Q.} and Tsang, {Tate T.H.}",

note = "Funding Information: The work was partially supportedb y the National ScienceF oundation (NSF/KY EPSCoR program) and the Center for Computational Sciences at the University of Kentucky. TTT is also partially supported by a grant from the U.S. Environmental Protection Agency. The authors appreciatet he reviewerst horough and thoughtfulc ommentsa nd suggestionsw hich helped us to improve this paper.",

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AU - Tsang, Tate T.H.

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PY - 1997/1/30

Y1 - 1997/1/30

N2 - Numerical solutions of 3-D time-dependent Rayleigh-Bénard convection are presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh numbers Ra = 8 × 103, 2.4 × 104 and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, 'T-shaped' rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.

AB - Numerical solutions of 3-D time-dependent Rayleigh-Bénard convection are presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh numbers Ra = 8 × 103, 2.4 × 104 and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, 'T-shaped' rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.

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Temporal, spatial and thermal features of 3-D Rayleigh-Bénard convection by a least-squares finite element method

Abstract

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