α Regularization of the POD-Galerkin dynamical systems of the Kuramoto–Sivashinsky equation

Sabetghadam, Fereidoun; Jafarpour, Alireza

doi:10.1016/j.amc.2011.11.083

Cited by 40 publications

(69 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Overall, the AD-ROM results are similar to those for the EV-ROMs in [14] and Reg-ROMs in [37,38]: For example, the accuracy of the AD-ROM energy spectrum (see Fig. 1 in this paper) is similar to the accuracy of the energy spectra of the best EV-ROMs (see Fig.…”

Section: Comparison With Other Romssupporting

confidence: 64%

“…Thus, while needed, this comparison is beyond the scope of this paper. We will, however, present next a brief qualitative comparison of the AD-ROM with two other representative classes of ROMs: the EV-ROMs [3,8,14] and the Reg-ROMs [37,38]. Since both the test problem and the statistics used in [14,38] are identical to those used in this paper, our qualitative comparison is meaningful.…”

Section: Comparison With Other Romsmentioning

confidence: 99%

“…Later, it was also used in a ROM context to develop regularized ROMs: The ROM-DF was first used in [37] for the 1D Kuramoto-Sivashinsky equation in a periodic setting. The ROM-DF was subsequently used in [38] for the 3D NSE in a general non-periodic setting.…”

Section: Explicit Rom Spatial Filteringmentioning

confidence: 99%

“…We emphasize, however, that our approach is fundamentally different, since we explicitly use spatial filters in the actual ROMs, i.e., we modify the mathematical model, not the input data. To our knowledge, explicit ROM spatial filtering has only be used in [14,37,38].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximate deconvolution reduced order modeling

Xie

Wells

Wang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Highlights• A new large eddy simulation reduced order model (LES-ROM) framework.• A new approximate deconvolution ROM (AD-ROM) not of eddy viscosity type.• Successful application of AD-ROM to 3D flow past cylinder at Re = 1000. AbstractThis paper proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of convection-dominated flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a ROM differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the three-dimensional flow past a circular cylinder at a Reynolds number Re = 1000.

show abstract

Section: Comparison With Other Romssupporting

confidence: 64%

Section: Comparison With Other Romsmentioning

confidence: 99%

Section: Explicit Rom Spatial Filteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate deconvolution reduced order modeling

Xie

Wells

Wang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…However, the use of POD/Galerkin methods raises numerical instability and non-linearity inefficiency problems [11,12,13,14]. Several methods have been presented to improve the numerical stability of ROMs, such as calibration [15,16], Fourier expansion [17], regularisation [18] and Petrov−Galerkin methods [2,19]. In order to enhance the nonlinear efficiency, various methods have been proposed, including empirical interpolation method (EIM) [20], the discrete version of EIM (DEIM) [14], quadratic expansion method [21,22], a hybrid of DEIM and quadratic expansion (residual DEIM) method [23], a Petrov−Galerkin projection method [15], and Gauss-Newton with approximated tensors (GNAT) method [24].…”

Section: Introductionmentioning

confidence: 99%

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Xiao¹,

Yang²,

Fang

et al. 2017

Journal of Computational Physics

View full text Add to dashboard Cite

This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the MohrCoulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.

show abstract

Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation

Xiao

Fang

Pain

et al. 2015

Numerical Methods in Fluids

157

136

View full text Add to dashboard Cite

Summary We present a new non‐intrusive model reduction method for the Navier–Stokes equations. The method replaces the traditional approach of projecting the equations onto the reduced space with a radial basis function (RBF) multi‐dimensional interpolation. The main point of this method is to construct a number of multi‐dimensional interpolation functions using the RBF scatter multi‐dimensional interpolation method. The interpolation functions are used to calculate POD coefficients at each time step from POD coefficients at earlier time steps. The advantage of this method is that it does not require modifications to the source code (which would otherwise be very cumbersome), as it is independent of the governing equations of the system. Another advantage of this method is that it avoids the stability problem of POD/Galerkin. The novelty of this work lies in the application of RBF interpolation and POD to construct the reduced‐order model for the Navier–Stokes equations. Another novelty is the verification and validation of numerical examples (a lock exchange problem and a flow past a cylinder problem) using unstructured adaptive finite element ocean model. The results obtained show that CPU times are reduced by several orders of magnitude whilst the accuracy is maintained in comparison with the corresponding high‐fidelity models. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

α Regularization of the POD-Galerkin dynamical systems of the Kuramoto–Sivashinsky equation

Cited by 40 publications

References 35 publications

Approximate deconvolution reduced order modeling

Approximate deconvolution reduced order modeling

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation

Contact Info

Product

Resources

About