Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives

Hijazi, Saddam; Stabile, Giovanni; Mola, Andrea; Rozza, Gianluigi

doi:10.1007/978-3-030-48721-8_10

Cited by 10 publications

(11 citation statements)

References 34 publications

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“…For the lifting function method, it is often problematic to determine suitable lifting functions that are physical. Ideally, the lifting functions are orthogonal to each other as in the work of Hijazi et al [53] who studied a flow past an airfoil with parameterized angle of attack and inflow velocity. They used two lifting functions with orthogonal inflow conditions: ζ c 1 = (0,1) and ζ c 2 = (1,0) on Γ i , respectively.…”

Section: Discussionmentioning

confidence: 99%

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A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

Star¹

2021

CICP

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A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation.The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order models are 270-308 times faster than the full order models for the lid driven cavity test case and 13-24 times for the Y-junction test case.

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Section: Discussionmentioning

confidence: 99%

“…Alternatively, the solution of the stationary version of the considered problem can be computed [49]. Two other common approaches are solving a non-homogeneous Stokes problem [46,50,51] or solving a potential flow problem [52,53].…”

Section: The Lifting Function Methodsmentioning

confidence: 99%

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

Star¹

2021

CICP

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“…In these circumstances, an additional effort has to be made for the treatment of the inhomogeneous velocity boundary conditions at the ROM level. The common strategies for tackling this issue are the lifting function method [39,40,50] and the penalty method [21,5,13,59,87]. A brief description of the two methods will be given and then the strategy of incorporating them inside the PINN formulation will be addressed.…”

Section: The Reduced Order Model (Rom)mentioning

confidence: 99%

POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations

Hijazi,

Freitag,

Landwehr

2021

Preprint

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We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by two cases which are the steady flow around a backward step and the unsteady turbulent flow around a surface mounted cubic obstacle.

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“…In the top image, we show the wall shear stress along the x direction, at time t = 50s, computed using full-order solver. In the bottom, we show the wall shear stress along x direction reconstructed at time t = 50s using 30 snapshots equispaced in the temporal window [1,30]. solution of a parametric PDE.…”

Section: Proper Orthogonal Decomposition With Interpolationmentioning

confidence: 99%

An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics

Tezzele,

Demo,

Mola

et al. 2018

Preprint

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In this work we present an integrated computational pipeline involving several model order reduction techniques for industrial and applied mathematics, as emerging technology for product and/or process design procedures. Its data-driven nature and its modularity allow an easy integration into existing pipelines. We describe a complete optimization framework with automated geometrical parameterization, reduction of the dimension of the parameter space, and nonintrusive model order reduction such as dynamic mode decomposition and proper orthogonal decomposition with interpolation. Moreover several industrial examples are illustrated.

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Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives

Cited by 10 publications

References 34 publications

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations

An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics

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