Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

Xiao, Dunhui; Fang, F.; Buchan, Andrew G.; Pain, Christopher C.; Navon, I. M.; Du, Juan; Hu, Gang

doi:10.1016/j.jcp.2014.01.011

Cited by 141 publications

(98 citation statements)

References 29 publications

(31 reference statements)

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“…Using this yet to be determined matrix (9), the basis interpolation of (8) can be made invertible and thus solvable…”

Section: B Discrete Empirical Interpolation Methodsmentioning

confidence: 99%

Nonlinear Model Reduction for Truss Frame Based on POD-DEIM

Cui¹,

Gong²,

Yu³

et al. 2017

Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017)

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Abstract-Nonlinear model simplification is an important part of many applications, such as flow control, optimization and statistical analysis. In this article, we summarize the POD-DEIM method to solve the nonlinear system of the truss frame .And use an example of a clamped beam to illustrate the DEIM specific simplification process with images which can intuitively observe the image of the specific selection process. The application of the method to the truss frame to verify the correctness of the study. The results show that POD-DEIM is able to approximate fully nonlinear behavior of geometrically nonlinear finite element models with good accuracy.

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“…Using this yet to be determined matrix (9), the basis interpolation of (8) can be made invertible and thus solvable…”

Section: B Discrete Empirical Interpolation Methodsmentioning

confidence: 99%

Nonlinear Model Reduction for Truss Frame Based on POD-DEIM

Cui¹,

Gong²,

Yu³

et al. 2017

Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017)

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“…In all the test cases presented in this work, the small dimension (N < 10) of the reduced space did not lead to such problem. Yet, if richer reduced spaces are used, possible alternatives to the present approach could be using EIM-DEIM [32,33] approaches or Gappy-POD [34].…”

Section: Rom For Velocity -Momentum Equationmentioning

confidence: 99%

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Stabile

Hijazi

Mola

et al. 2017

Communications in Applied and Industrial Mathematics

142

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Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible flow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

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“…The methods of improving the stability of the ROM can be found in [32,56,48,23,24,52]. The approaches of enhancing the non-linearity efficiency have been developed in the work of [14,4,19,20,51,12].…”

Section: Introductionmentioning

confidence: 99%

A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

Xiao¹,

Fang²,

Pain³

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (Ω p ∈ R P ). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over Ω p can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique [50,53] where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space.The new P-NIROM technique has been applied to parameterized Navier-Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out.

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Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

Cited by 141 publications

References 29 publications

Nonlinear Model Reduction for Truss Frame Based on POD-DEIM

Nonlinear Model Reduction for Truss Frame Based on POD-DEIM

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

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