Non-intrusive reduced order modelling of the Navier–Stokes equations

Xiao, Dunhui; Fang, F.; Buchan, Andrew G.; Pain, Christopher C.; Navon, I. M.; Muggeridge, Ann

doi:10.1016/j.cma.2015.05.015

Cited by 136 publications

(91 citation statements)

References 32 publications

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“…In order to tackle these issues in intrusive ROMs, a number of non-intrusive reduced order models (NIROMs) have been developed recently [50,53,35,34]. However, very little work can be found addressing non-intrusive model reduction for parameterized PDEs, where inputs (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, we have developed three types of NIROMs based on Taylor series expansion, Smolyak sparse grid and radial basis function (RBF) methods [50,53]. The NIROMs have been successfully applied to some realistic problems such as fluid and solid interaction [55] and porous media multi-phase problems [54].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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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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102

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

102

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“…A number of non-intrusive reduced order methods have been proposed, such as a black-box stencil interpolation method [32], a POD-RBF method for unsteady fluid flows [33], a Taylor series and Smolyak sparse grid method for the NavierStokes equations [34], a two-level NIROM based on POD-RBF method for nonlinear parametrized PDEs [35,36,33], a POD-RBF for the Navier-Stokes equations [37]. NIROMs have also been applied to realistic problems such as multi-phase flow in porous media problems [38] and incompressible fluids and solids without fracturing problems [39].…”

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

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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.

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Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids

Xiao

Lin

Fang

et al. 2016

Numerical Methods in Fluids

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SUMMARYIn this article, we describe a non-intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non-intrusive reduced order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non-intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hyper-surfaces representing the reduced porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element (CVFEM) multiphase model. Numerical examples show that the NIROM accuracy relative to the high fidelity model is maintained whilst the computational cost is reduced by several orders of magnitude.

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Non-intrusive reduced order modelling of the Navier–Stokes equations

Cited by 136 publications

References 32 publications

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

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

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

Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids

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