L<scp>OW</scp>-D<scp>IMENSIONAL</scp> M<scp>ODELING AND</scp> N<scp>UMERICAL</scp> S<scp>IMULATION OF</scp> T<scp>RANSITION IN</scp> S<scp>IMPLE</scp> S<scp>HEAR</scp> F<scp>LOWS</scp>

Rempfer, Dietmar

doi:10.1146/annurev.fluid.35.030602.113908

Cited by 80 publications

(51 citation statements)

References 145 publications

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“…If, instead, s = 10~4 (Fig. 5(iii)) and (5 NC = 0.5, then the number of needed / NC intervals increases to twelve (which decreases the compression factor to 1.66), with numbers of modes oscillating between (n,n-¡) = (8,10) and (7,15). Of course, the number of / N c intervals can be decreased taking larger / NC lengths, as shown in Fig.…”

Section: The Basic Local Pod Plus Galerkin Projection Methodsmentioning

confidence: 99%

“…Reduced order models (ROMs) are receiving a continuously increasing attention in the literature due to their interest in both understanding basic mechanisms of fluid systems [8,15,16] and improving prediction and design in industrial processes [5,12,21 ]. Concerning the latter, the need of reducing development time and cost in industry is nowadays enhancing a trend to substitute wind tunnel experiments by numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

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Reduced order models based on local POD plus Galerkin projection

Rapún

Vega

2010

Journal of Computational Physics

105

101

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A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduced that reduce computational complexity and deal with: (a) updating the POD manifold (instead of calculating it) at the end of each Galerkin interval; (b) using only a limited number of mesh points to calcúlate the right hand side of the Galerkin system; and (c) introducing a second error estímate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur during the application of the Galerkin system. The resulting method, called local POD plus Galerkin projection method, turns out to be both robust and efficient. For illustration, we consider a time-dependent Fisher-like equation and a complex Ginzburg-Landau equation.

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Section: The Basic Local Pod Plus Galerkin Projection Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced order models based on local POD plus Galerkin projection

Rapún

Vega

2010

Journal of Computational Physics

105

101

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“…2 is exceeded). This process-referred to as bypass transition [22,23]-has been suggested as a critical factor in shear-flow transition to account for discrepancies between experimental findings and analytical forecasts based on normal modes [24]. The second key point is that transient growth can occur on time scales that are comparable to those of the studied process.…”

Section: Introductionmentioning

confidence: 96%

River bedform inception by flow unsteadiness: A modal and nonmodal analysis

et al. 2016

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River bedforms arise as a result of morphological instabilities of the stream-sediment interface. Dunes and antidunes constitute the most typical patterns, and their occurrence and dynamics are relevant for a number of engineering and environmental applications. Although flow variability is a typical feature of all rivers, the bedform-triggering morphological instabilities have generally been studied under the assumption of a constant flow rate. In order to partially address this shortcoming, we here discuss the influence of (periodic) flow unsteadiness on bedform inception. To this end, our recent one-dimensional validated model coupling Dressler's equations with a refined mechanistic sediment transport formulation is adopted, and both the asymptotic and transient dynamics are investigated by modal and nonmodal analyses.

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“…Myriad of successful ROMs have been developed for a large range of fluid flows [36,53]. Most ROMs fall in the category of data-driven Galerkin models [17], the focus of this study.…”

Section: Introductionmentioning

confidence: 99%

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Stankiewicz

Morzyński

Kotecki

et al. 2016

Theor. Comput. Fluid Dyn.

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We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

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LOW-DIMENSIONAL MODELING AND NUMERICAL SIMULATION OF TRANSITION IN SIMPLE SHEAR FLOWS

Cited by 80 publications

References 145 publications

Reduced order models based on local POD plus Galerkin projection

Reduced order models based on local POD plus Galerkin projection

River bedform inception by flow unsteadiness: A modal and nonmodal analysis

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

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