A zonal Galerkin-free POD model for incompressible flows

Bergmann, Michel; Ferrero, Andrea; Iollo, Angelo; Lombardi, Edoardo; Scardigli, Angela; Telib, Haysam

doi:10.1016/j.jcp.2017.10.001

Cited by 36 publications

(30 citation statements)

References 52 publications

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“…In this work, to address the above problems, we used a Galerkin‐free method to construct the POD‐ROM for flow in fractured porous media. The Galerkin‐free (or equation‐free) method is designed for the efficient coarse‐grained computational study of complex problems . Sirisup et al presented a Galerkin‐free POD‐assisted method to simulate the incompressible Navier‐Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

“…The results demonstrated that the Galerkin‐free ROM procedure is robust for large mesh deformations while maintaining high accuracy. Bergmann et al coupled a high‐fidelity simulation and a Galerkin‐free POD method for a zonal simulation of general flow fields. The obtained results from two test cases showed that the proposed approach could be applied to perform predictive simulations.…”

Section: Introductionmentioning

confidence: 99%

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A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

Han

Tang

et al. 2020

Energy Science & Engineering

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Using traditional high‐fidelity numerical simulation to simulate fluid flow in fractured porous media in a real field remains challenging. It involves a large number of degrees of freedom when matrix and fracture equations are solved. To address this challenge, we propose a Galerkin‐free framework to construct a reduced‐order model (ROM) based on the proper orthogonal decomposition (POD). Compared with the typical POD‐based modeling process commonly used in previous studies, the POD‐ROM can be built without performing the Galerkin projection of flow equations onto the low‐dimensional space spanned by the POD basis functions. The numerical integration method was incorporated to obtain the POD time coefficients based on the flow equations solved by the conventional finite volume method. Two complex fracture cases reflecting high‐contrast porous media in a two‐dimensional domain were designed to verify the accuracy and efficiency of the established Galerkin‐free POD‐ROM. Sensitivity analysis of parameters was conducted to examine the adaptability of the ROM. The results illustrate that, compared with the fine‐scale model, the ROM can significantly reduce the CPU time without compromising the quality of the numerical solutions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

Han

Tang

et al. 2020

Energy Science & Engineering

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“…We use the initial condition u ( x ,0) = u 0 ( x ) and (for simplicity) homogeneous Dirichlet boundary conditions u ( x , t ) = 0 . ROMs have been used to reduce the computational cost of scientific and engineering applications that are governed by relatively few recurrent dominant spatial structures . In an off‐line stage, full‐order model (FOM) data on a given time interval are used to build the ROM.…”

Section: Introductionmentioning

confidence: 99%

“…ROMs have been used to reduce the computational cost of scientific and engineering applications that are governed by relatively few recurrent dominant spatial structures. [1][2][3][4][5][6][7][8][9][10][11][12] In an off-line stage, full-order model (FOM) data on a given time interval are used to build the ROM. In an online stage, ROMs are repeatedly used for parameter settings and/or time intervals that are different from those used to build them.…”

Section: Introductionmentioning

confidence: 99%

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

Mohebujjaman

Rebholz

Iliescu

2018

Numerical Methods in Fluids

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Summary We have recently proposed a data‐driven correction reduced‐order model (DDC‐ROM) framework for the numerical simulation of fluid flows, which can be formally written as follows. The new DDC‐ROM was constructed by using reduced‐order model spatial filtering and data‐driven reduced‐order model closure modeling (for the Correction term) and was successfully tested in the numerical simulation of a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. In this paper, we propose a physically constrained DDC‐ROM (CDDC‐ROM), which aims at improving the physical accuracy of the DDC‐ROM. The new physical constraints require that the CDDC‐ROM operators satisfy the same type of physical laws (ie, the Correction term's linear component should be dissipative, and the Correction term's nonlinear component should conserve energy) as those satisfied by the fluid flow equations. To implement these physical constraints, in the data‐driven modeling step, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDC‐ROM and standard DDC‐ROM for a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. To this end, we consider a reproductive regime as well as a predictive (ie, cross‐validation) regime in which we use as little as 50% of the original training data. The numerical investigation clearly shows that the new CDDC‐ROM is significantly more accurate than the DDC‐ROM in both regimes.

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“…Reduced Order Models have been extensively investigated as low cost prediction methods in several fields of engineering. As far as fluid mechanics is concerned there are several different approaches: Proper Orthogonal Decomposition (POD) [15,18,20,31,36,42,43,46,47,53], Proper Generalised Decomposition (PGD) [22], Reduced Basis (RB) [40,41], Dynamic Mode Decomposition [45], Grassmannian interpolation [4], Empirical Interpolation Method (EIM) [9], Discrete Empirical Interpolation Method (DEIM) [21], hyper-reduction [6,44,54], regularized ROM [52], domain decomposition approaches [8,13,16]. In this work the attention is focused on the use of POD for the prediction of compressible steady flows described by the Euler equations or by the Reynolds Averaged Navier-Stokes (RANS) equations.…”

Section: Introductionmentioning

confidence: 99%

Global and local POD models for the prediction of compressible flows with DG methods

Ferrero

Iollo

Larocca

2018

Numerical Meth Engineering

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Proper Orthogonal Decomposition (POD) allows to compress information by identifying the most energetic modes obtained from a database of snapshots. In this work, POD is used to predict the behavior of compressible flows by means of global and local approaches which exploit some features of a discontinuous Galerkin spatial discretization. The presented global approach requires the definition of high-order and low-order POD bases which are built from a database of high-fidelity simulations. Predictions are obtained by performing a cheap low-order simulation whose solution is projected on the low-order basis. The projection coefficients are then used for the reconstruction with the high-order basis. However, the non-linear behavior related to the advection term of the governing equations makes the use of global POD bases quite problematic. For this reason, a second approach is presented in which an empirical POD basis is defined in each element of the mesh. This local approach is more intrusive with respect to the global approach but it is able to capture better the non-linearities related to advection. The two approaches are tested and compared on the inviscid compressible flow around a gas-turbine cascade and on the compressible turbulent flow around a wind turbine airfoil.

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A zonal Galerkin-free POD model for incompressible flows

Cited by 36 publications

References 52 publications

A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

Global and local POD models for the prediction of compressible flows with DG methods

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