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

Salinger, Andrew G.; Lehoucq, Richard B.; Pawlowski, Roger P.; Shadid, John N.

doi:10.1002/fld.392

Cited by 31 publications

(32 citation statements)

References 27 publications

(34 reference statements)

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“…[5], or by computing the stability of the fixed points obtained by continuation methods (see [4,[6][7][8][9], among others). In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Meth. Fluids (see [3,8,[12][13][14][15], among others). To compare the results several point data, temporal and spatial time averages, and fluctuations with respect to the mean values, of the velocity, vorticity, pressure differences and temperature were supplied by the contributors, in addition to the period, mean heat flux transport on the lateral boundaries, or a metric to measure the loss of the center-symmetry of the temperature field, although the full description of the solutions of this problem remained open.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Periodic orbits in tall laterally heated rectangular cavities

Net

Umbría

2017

Phys. Rev. E

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This study elucidates the origin of the multiplicity of stable oscillatory flows detected by time integration in tall rectangular cavities heated from the side. By using continuation techniques for periodic orbits, it is shown that initially unstable branches, arising at Hopf bifurcations of the basic steady flow, become stable after crossing Neimark-Sacker points. There are no saddlenode or pitchfork bifurcations of periodic orbits, which could have been alternative mechanisms of stabilization. According to the symmetries of the system, the orbits are either fixed cycles, which retain at any time the center-symmetry of the steady flow, or symmetric cycles involving a time shift in the global invariance of the orbit. The bifurcation points along the branches of periodic flows are determined. By using time integrations, with unstable periodic solutions as initial conditions, it is found out which of the bifurcations at the limits of the intervals of stable periodic orbits are sub or supercritical.PACS numbers: 47.15.-x, 47.20.-k

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“…[5], or by computing the stability of the fixed points obtained by continuation methods (see [4,[6][7][8][9], among others). In Ref.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Periodic orbits in tall laterally heated rectangular cavities

Net

Umbría

2017

Phys. Rev. E

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“…The algorithms are chosen to work with codes that use Newton's method to reach steady solutions and to have minimal additional interfacing requirements over the nonlinear solver. Furthermore, they are designed for scalability to large problems, such as those that arise from discretizations of partial differential equations, and to run on distributed memory parallel machines [Salinger et al 2002].…”

Section: Loca: Library Of Continuation Algorithmsmentioning

confidence: 99%

An overview of the Trilinos project

Heroux

Bartlett

Howle

et al. 2005

ACM Trans. Math. Softw.

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939

671

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The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multi-physics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) Providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking.Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates highquality software engineering practices that are increasingly required from simulation software.

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“…For more information on these algorithms, consult [14], [20], [21]. Branch switching was accomplished using an algorithm which perturbs the symmetric, unstable solution in the direction of the null vector, φ:…”

Section: Numerical Techniquementioning

confidence: 99%

A Multiparameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid

Bou-Rabee¹,

Romero²,

Salinger³

2002

SIAM J. Appl. Dyn. Syst.

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Abstract. In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which confirm our intuition as well as the work of others. The numerical bifurcation results obtained from applying the Library of Continuation Algorithms (LOCA) reveal a plethora of one, two, and higher codimension bifurcations. For a vertical or standing cantilever beam, bifurcations to buckled solutions (via symmetry breaking) and oscillating solutions are detected as a function of gravity and the fluid-structure interaction. The unfolding of these results as a function of the orientation of the beam compared to gravity is also revealed.

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

Cited by 31 publications

References 27 publications

Periodic orbits in tall laterally heated rectangular cavities

Periodic orbits in tall laterally heated rectangular cavities

An overview of the Trilinos project

A Multiparameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid

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