Computational predictability of natural convection flows in enclosures

Christon, Mark A.; Gresho, P. M.; Sutton, Steven B.

doi:10.1016/b978-008043944-0/50941-0

Cited by 27 publications

(56 citation statements)

References 3 publications

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“…In this section we use the terms centro-symmetric to describe eigenmodes that preserve the symmetry of the equations and boundary conditions, as described in reference [1], and symmetry-breaking to describe those that break the centro-symmetry.…”

Section: Application Of Scalable Stability Analysis Algorithmsmentioning

confidence: 99%

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Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Salinger

Lehoucq

Pawlowski

et al. 2002

Numerical Methods in Fluids

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Summary:Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability analysis are used to study transition from steady to transient flow as a function of Rayleigh number. To carry out this study the steady state form of the governing PDEs is discretized using a Galerkin/Least Squares Finite Element formulation, and solved on parallel computers using a fully coupled Newton method and preconditioned Krylov iterative linear solvers. Linear stability analysis employing a large scale eigenvalue capability is used to determine the stability of the steady solutions. The boundary between steady and time dependent flows is determined by a Hopf bifurcation tracking capability that is used to directly track the instability with respect to the aspect ratio of the system and with respect to mesh resolution. The effect of upwinding stabilization terms in the finite element formulation on the computed value of critical Rayleigh number is investigated. The Hopf bifurcation signaling the onset of flow is determined to occur at a critical Rayleigh number of .

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Section: Application Of Scalable Stability Analysis Algorithmsmentioning

confidence: 99%

“…The model problem is fully described in reference [1]. The computational method employs a robust steady state 1 …”

Section: Introductionmentioning

confidence: 99%

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Salinger

Lehoucq

Pawlowski

et al. 2002

Numerical Methods in Fluids

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“…The data of the problem can be found in [5]. The interest of this problem in that it displays transition to chaos as the Rayleigh number is increased.…”

Section: Numerical Dissipationmentioning

confidence: 99%

Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modeling

Codina¹,

Principe²,

Ávila³

2010

International Journal of Numerical Methods for Heat & Fluid

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“…With the appropriate dimensionless coefficients per the problem definition, the MELT2D code solves Eqns. (1)-(3) as given in [1].…”

Section: The Melt2d Codementioning

confidence: 99%

Thermally driven flow in a cavity using the Galerkin finite element method

Westerberg¹

2001

Computational Fluid and Solid Mechanics

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Time periodic solutions are found for the natural convection of a Pr=0.71 fluid in a differentially heated 8x1 cavity at Ra=3.4x10 5 using a "straight" Galerkin finite element method with the Q 2 Q 1 element. Time integration is performed with an implicit second-order accurate (in time) trapezoid rule. As expected, the average values of various solution metrics were relatively insensitive to mesh refinement and time integration truncation error, although coarse meshes tend to damp out the time periodic behavior. The amplitude and frequency of the oscillation is sensitive to both mesh and time truncation errors.

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Computational predictability of natural convection flows in enclosures

Cited by 27 publications

References 3 publications

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modeling

Thermally driven flow in a cavity using the Galerkin finite element method

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