The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows

By Bernd R. Noack, P. Papas, P. Monkewitz. Journal of Fluid Mechanics, 2005

403 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/beb26e8cf5b49ed7df06dbcd3201300f9facfc80

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, background): “We note that, since the computational domain that we consider is large enough, the pressure terms in (7) can be neglected (for details, see [37,56]).”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, background): “It is known that neglecting the pressure term for convectively unstable shear layers, especially ones with two-dimensional mixing layers, can result in large errors as was demonstrated in [96].”
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators (2009, methodology): “Alternately, the balanced models, which accurately capture the transient dynamics, could be combined with the POD-based models using shift modes of Noack et al. (2005) which accurately capture vortex shedding and some of the transient dynamics.”
Cluster-based reduced-order modelling of a mixing layer (2013, methodology): “For such data, POD generally yields cosine- and sine-like wave pairs for the first and higher frequency harmonics (Deane et al. 1991; Rempfer & Fasel 1994; Noack et al. 2005).”
On the stability and extension of reduced-order Galerkin models in incompressible flows (2009, background): “Hence, the pressure is neglected on the outflow boundary so the pressure term vanishes in the reduced-order model [ 31 ].”
Model Reduction for Flow Analysis and Control (2017, background): “In some cases, one does need to consider a pressure term (e.g., Noack et al. 2005; Holmes et al. 2011, section 4.3), but in many cases, the pressure drops out altogether, as a consequence of the divergence theorem.”
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body (2013, methodology): “In this study, νTi is derived from the modal power balance (Noack et al. 2005).”
POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations (2016, methodology): “(48) is similar to the system obtained if we apply a modal eddy viscosity [34,56,62].”
Enablers for robust POD models (2009, positive): “However, Noack [11] proved that neglecting the pressure term for convectively unstable shear layers (as the mixing layer or the wake ﬂow) can lead to large amplitude errors in the Galerkin model.”
Fluid flow dynamics under location uncertainty (2013, positive): “Nevertheless, the constructed system reveals often unstable in practice and does not allow operating long term forecasts even if it fits perfectly to the data (Noack et al. 2005, Artana et al. 2012).”
Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data (2016, neutral): “Compared to alternating methods, the POD conducts one iteration (returning with m = 1, since 23 it corresponds to the time variable), and hence requires either an explicit elimination of boundary conditions 24 [3], or nonlinear corrections [41].”