Reduced order models based on local POD plus Galerkin projection

Rapún, María-Luisa; Vega, José M.

doi:10.1016/j.jcp.2009.12.029

Cited by 105 publications

(102 citation statements)

References 23 publications

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“…In [41], some residual based POD modes were added to the old POD subspace for Navier-Stokes equations. In [42], a second error estimate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur was introduced. In this case, two reduced systems must be solved at a time, thus incurring higher computational cost.…”

Section: Algorithm 1 Adaptive Local-global Pod Model Order Reduction mentioning

confidence: 99%

Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

2016

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Abstract:We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.

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Section: Algorithm 1 Adaptive Local-global Pod Model Order Reduction mentioning

confidence: 99%

Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

2016

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“…The method introduced in Rapiin and Vega (2010) represents a somewhat different approach to the field, resulting from a critical view of the POD-based reduction techniques. The local POD plus Galerkin projection (LPOD+GP) method shares a few ingredients with some of the adaptive methods cited above, but exploits new ideas based on two main observations.…”

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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“…This method may exhibit instability due to higher order modes truncation, which is the object of current research. [24][25][26][27][28][29] If instability is avoided, the root mean square (RMS) error of the solution of the resulting model retaining n modes is readily calculated in terms of the POD singular values as σ 2 n+1 + σ 2 n+2 + . .…”

Section: B Low Dimensional Modeling Of Streaksmentioning

confidence: 99%

Low-dimensional modeling of streaks in a wedge flow boundary layer

Higuera

Vega

2012

Physics of Fluids

Self Cite

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This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

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Reduced order models based on local POD plus Galerkin projection

Cited by 105 publications

References 23 publications

Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

Reduced order modeling of some fluid flows of industrial interest

Low-dimensional modeling of streaks in a wedge flow boundary layer

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