POD Applied to Numerical Study of Unsteady Flow Inside Lid-Driven Cavity

Lestandi, Lucas

doi:10.4208/jms.v51n2.18.03

Cited by 4 publications

(4 citation statements)

References 38 publications

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“…3, indicates multiple bifurcations originating at different Re's. Thus, it is imperative that one identifies the target Re in the same segment of donor Re's for DNSquality reconstruction for flow past circular cylinder as in SHPG and for flow inside LDC in [17]. In each of these sectors of Re, the flow behaves similarly and the (St, Re)-relation is distinct.…”

Section: Need For Time Scalingmentioning

confidence: 99%

“…Consequently, in this paper, we rely on previously established bifurcation diagram (see Refs. [17,37] for details) to bound the ROM domain.…”

Section: Introductionmentioning

confidence: 99%

“…While the flow past a circular cylinder displays a single dominant peaks with side bands in the spectrum (shown on the right hand side frames), the flow inside LDC clearly demonstrates multiple peaks. This property has been explored thoroughly for the LDC in [17] to explain the roles of multiple POD modes.…”

Section: Introductionmentioning

confidence: 99%

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Reduced order model of flows by time-scaling interpolation of DNS data

Sengupta

Lestandi

Haider

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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A new reduced order model (ROM) is proposed here for reconstructing super-critical flow past circular cylinder and lid driven cavity using time-scaling of vorticity data directly. The present approach is a significant improvement over instability-mode (developed from POD modes) based approach implemented in Sengupta et al. [Phys Rev E 91(4):043303, 2015], where governing Stuart-Landau-Eckhaus equations are solved. In the present method, we propose a novel ROM that uses relation between Strouhal number (St) and Reynolds number (Re). We provide a step by step approach for this new ROM for any Re and is a general procedure with vorticity data requiring very limited storage as well as being extremely fast. We emphasize on the scientific aspects of developing ROM by taking data from close proximity of the target Re to produce DNS-quality reconstruction, while the applied aspect is also shown. All the donor points need not be immediate neighbors and the reconstructed solution has equivalent relaxed accuracy. However, one would restrain the range where the flow behavior is coherent between donors. The reported work is a proof of concept utilizing the external and internal flow examples, and this can be extended for other flows characterized by appropriate Re-St data.

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Section: Need For Time Scalingmentioning

confidence: 99%

“…Consequently, in this paper, we rely on previously established bifurcation diagram (see Refs. [17,37] for details) to bound the ROM domain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reduced order model of flows by time-scaling interpolation of DNS data

Sengupta

Lestandi

Haider

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

Self Cite

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“…Their use in numerous engineering problems have made it essential tools for quasi-real-time simulation and control of complex problems (see . Notable applications are fluid mechanics, [5][6][7][8][9] fluid-structure interaction, [10][11][12][13] and structural or material mechanics. [14][15][16] Basically, it consists in the approximation of a problem with a very large number of degrees of freedom (typically several thousands to millions) by a model with at most one hundred of degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Neville–Aitken interpolation algorithm on Grassmann manifolds: Applications to reduced order model

Hamidi

Hamdouni

Falaize

2021

Numerical Methods in Fluids

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An extension of the well-known Neville-Aitken's algorithm for interpolation on the Grassmann manifold G m (R n ) in the framework of parametric model order reduction is presented. Interpolation points on G m (R n ) are the subspaces spanned by bases obtained by Proper Orthogonal Decomposition of available solutions associated with the chosen parameter sampling. The Neville-Aitken's algorithm is performed recursively via the geodesic barycenter of two points. Three CFD applications are presented: (i) the Von Karman vortex shedding street, (ii) the lid-driven cavity with inflow and (iii) the flow induced by a rotating solid. Numerical results are relevant with respect to accuracy while the asymptotic complexity is comparable to the state of the art.

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Low Rank Approximation of Multidimensional Data

Azaïez

Lestandi

Rebollo

2019

High-Performance Computing of Big Data for Turbulence and Combustion

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In the last decades, numerical simulation has experienced tremendous improvements driven by massive growth of computing power. Exascale computing has been achieved this year and will allow solving ever more complex problems. But such large systems produce colossal amounts of data which leads to its own difficulties. Moreover, many engineering problems such as multiphysics or optimisation and control, require far more power that any computer architecture could achieve within the current scientific computing paradigm. In this chapter, we propose to shift the paradigm in order to break the curse of dimensionality by introducing decomposition to reduced data. We present an extended review of data reduction techniques and intends to bridge between applied mathematics community and the computational mechanics one.The chapter is organized into two parts. In the first one bivariate separation is studied, including discussions on the equivalence of proper orthogonal decomposition (POD, continuous framework) and singular value decomposition (SVD, discrete matrices). Then, in the second part, a wide review of tensor formats and their approximation is proposed. Such work has already been provided in the literature but either on separate papers or into a pure applied mathematics framework. Here, we offer to the data enthusiast scientist a description of Canonical, Tucker, Hierarchical and Tensor train formats including their approximation algorithms. When it is possible, a careful analysis of the link between continuous and discrete methods will be performed.

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POD Applied to Numerical Study of Unsteady Flow Inside Lid-Driven Cavity

Cited by 4 publications

References 38 publications

Reduced order model of flows by time-scaling interpolation of DNS data

Reduced order model of flows by time-scaling interpolation of DNS data

Generalization of the Neville–Aitken interpolation algorithm on Grassmann manifolds: Applications to reduced order model

Low Rank Approximation of Multidimensional Data

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