A low-dimensional model for simulating three-dimensional cylinder flow

By Xia L. Ma, G. Em Karniadakis. 2002

318 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

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Citations in the corpus

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, background): “…have appeared in the literature (Aubry et al. 1988; Podvin & Lumley 1998; Podvin 2001; Rempfer & Fasel 1994; Rempfer 1996; Cazemier et al. 1998; Ma & Karniadakis 2002; Sirisup & Karniadakis 2004; Buffoni et al. 2006; Noack et al. 2002, 2003, 2005, 2008; Ullmann & Lang 2010; Hay et al. 2009,…”
Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition (2009, methodology): “As an example, Ma & Karniadakis (2002) have successfully captured the three-dimensional bifurcation by building a basis consisting of both three- and two-dimensional POD modes extracted closely around the bifurcation point reported experimentally (note that it requires the knowledge of the…”
The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows (2005, methodology): “The transient behaviour can be properly described in the framework of empirical Galerkin models at the expense of significantly increasing the number of modes (Ma & Karniadakis 2002; Jørgensen, Sørensen & Brøns 2003; Noack et al. 2003; Bergmann, Cordier & Brancher 2004).”
A reduced‐order approach to four‐dimensional variational data assimilation using proper orthogonal decomposition (2007, unknown): “It was successfully used in a variety of fields including signal analysis and pattern recognition (see Fukunaga 1990), fluid dynamics and coherent structures (see Aubry et al. 1998; Bansch 1991.) and more recently in control theory (see Afanasiev, et al. 2001; Arian, et al. 2000; Ly and Tran 2002”
Efficient sensor placement for ocean measurements using low-dimensional concepts (2009, background): “In past work, in a series of papers (Dong et al., 2006 Ma and Karniadakis, 2002; Ma et al., 2000) have demonstrated the low-dimensionality of the turbulent wake in flow past a circular cylinder.”
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake (2003, methodology): “Following Deane et al. (1991) and Ma & Karniadakis (2002), the Galerkin projection of the pressure term is found to be negligible.”
Low-order modelling of laminar flow regimes past a confined square cylinder (2004, methodology): “Model predictions as a function of the Reynolds number We applied the POD technique to extract an optimal basis from a mixed database that contains snapshots at different Reynolds numbers, see Ma & Karniadakis (2002), and at a fixed blockage ratio of 1/8.”
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data (2018, background): “For the flow past a cylinder, if we simply increase the Reynolds number beyond a threshold value of ≈ 185 [30], the spanwise velocity w becomes more prominent due to the”
Computational Reduction for Parametrized PDEs: Strategies and Applications (2012, background): “The first applications of POD were concerned with the analysis of turbulent flows and date back to the early ’90s [1, 2]; more recent applications can be found, for instance, in [22,25,27,30], as well as in [9, 12,20] for parametrized flows.”
On the stability and extension of reduced-order Galerkin models in incompressible flows (2009, methodology): “and the divergence-free property, the pressure term drops out from Eq. (25) for the case of p = 0o n the outerflow boundary so [ 25 ].”