Using Automatic Differentiation to Create a Nonlinear Reduced-Order-Model Aerodynamic Solver

Thomas, Jeffrey P.; Dowell, Earl H.; Hall, Kenneth C.

doi:10.2514/1.36414

Cited by 49 publications

(23 citation statements)

References 17 publications

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“…These models have been developed mainly for unsteady flows that are either linear or weakly nonlinear perturbations of base flows, or they only deal with time periodic flows, intending to cope with stability and control issues. Some examples can be found in the work by Dowell and Hall (2001), Rempfer (2003), Lucia et al (2004), Lieu et al (2006), and Thomas et al (2010); the extension of these to general time-dependent, fully nonlinear flows in realistic industrial conditions has not been performed to our knowledge. Fully nonlinear, unsteady ROMs of simpler problems have received considerable attention in recent years (Couplet et al 2005;Rapun and Vega 2010), but these are still several steps behind their efficient industrial use.…”

Section: Introductionmentioning

confidence: 99%

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

et al. 2012

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Abstract:A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range 0.4 < Mach number < 0.8, -3° < angle of attack < 3°.

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Section: Introductionmentioning

confidence: 99%

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

et al. 2012

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“…Since then, an increasing number of works on the topic appeared in the literature approaching problems of scientific and industrial interest, taking advantage of the ability of such ROMs to drastically reduce the computational cost associated with the involved numerical simulations Thomas et al 2010). Unsteady ROMs are also used to speed up the calculation of steady states when these are computed as attractors at large times.…”

Section: Time-dependent Romsmentioning

confidence: 99%

Reduced order modeling of some fluid flows of industrial interest

Alonso

Terragni²,

Velázquez³

et al. 2012

Fluid Dyn. Res.

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Some basic ideas are presented for the construction of robust, computationally efficient reduced order models amenable to be used in industrial environments, combined with somewhat rough computational fluid dynamics solvers. These ideas result from a critical review of the basic principles of proper orthogonal decomposition-based reduced order modeling of both steady and unsteady fluid flows. In particular, the extent to which some artifacts of the computational fluid dynamics solvers can be ignored is addressed, which opens up the possibility of obtaining quite flexible reduced order models. The methods are illustrated with the steady aerodynamic flow around a horizontal tail plane of a commercial aircraft in transonic conditions, and the unsteady lid-driven cavity problem. In both cases, the approximations are fairly good, thus reducing the computational cost by a significant factor.

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“…POD-based ROMs are constructed to simulate both unsteady [6,[10][11][12][13][14][15] and steady, multiparameter [16][17][18][19][20] problems, taking advantage of the optimality of the POD modes. The standard method relies on early ideas by Sirovich [21], who suggested applying POD to a set of representative snapshots calculated offline by a standard NS along the considered time/parameter span.…”

Section: Introductionmentioning

confidence: 99%

Adaptive POD‐based low‐dimensional modeling supported by residual estimates

Rapún

Terragni

Vega

2015

Numerical Meth Engineering

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SUMMARYAn adaptive low-dimensional model is considered to simulate time-dependent dynamics in nonlinear dissipative systems governed by PDEs. The method combines an inexpensive POD-based Galerkin system with short runs of a standard numerical solver that provides the snapshots necessary to first construct and then update the POD modes. Switching between the numerical solver and the Galerkin system is decided 'on the fly' by monitoring (i) a truncation error estimate and (ii) a residual estimate. The latter estimate is used to control the mode truncation instability and highly improves former adaptive strategies that detected this instability by monitoring consistency with a second instrumental Galerkin system based on a larger number of POD modes. The most computationally expensive run of the numerical solver occurs at the outset, when the whole set of POD modes is calculated. This step is improved by using mode libraries, which may either be generic or result from former applications of the method. The outcome is a flexible, robust, computationally inexpensive procedure that adapts itself to the local dynamics by using the faster Galerkin system for the majority of the time and few, on demand, short runs of a numerical solver. The method is illustrated considering the complex Ginzburg-Landau equation in one and two space dimensions.

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Using Automatic Differentiation to Create a Nonlinear Reduced-Order-Model Aerodynamic Solver

Cited by 49 publications

References 17 publications

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

Reduced order modeling of some fluid flows of industrial interest

Adaptive POD‐based low‐dimensional modeling supported by residual estimates

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