Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

Star, Sabrina Kelbij; Sanderse, Benjamin; Stabile, Giovanni; Rozza, Gianluigi; Degroote, Joris

doi:10.1002/fld.4994

Cited by 7 publications

(3 citation statements)

References 85 publications

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“…We solely focus on the FEM as our discretization method and will introduce it in Section 3. Nevertheless, the method we describe in this paper is generalizable in a sense that FEM can be replaced by other similar methods, such as FVM [36,37].…”

Section: Related Workmentioning

confidence: 99%

A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices

Jóczik

Zimborás

Majoros³

et al. 2022

Applied Sciences

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Numerical simulations of physical systems are found in many industries, as they currently play a crucial role in product development. There are many numerical methods for solving differential equations that describe the underlying physics behind the mathematical models in the simulation, among which, the finite element method (FEM) is one of the most commonly used. Although in many applications the FEM seems to provide an acceptable solution to the problem, there are still many complex real-life processes that can be challenging to simulate numerically due to their complexity and large size. Recently, there has been a shift in research towards efficiently applying quantum algorithms in finite element analysis (FEA), as the potential and speedup that they could offer have been shown, but little to no effort has been made towards the applicability and cost efficiency of these algorithms in real-world quantum devices. In this paper, we propose a cost-efficient method for applying quantum algorithms in FEA for industrial problems post-processed by classical algorithms in order to address the limitations of available quantum hardware and their cost when accessing them through different cloud-based services. We carry this out by approximating the solution of the initially large system with a suitable quantum algorithm and using the obtained solutions to generate a set of reduced-order models (ROMs) that are much smaller in complexity and size than the original model. This allows the simulation of the original model with different parameter sets and excitations to be run efficiently on classical computers without having the need to access quantum subroutines again. This way, we have reduced the usage of quantum hardware (and thus the development cost) while still taking advantage of its quantum speedup.

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Section: Related Workmentioning

confidence: 99%

A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices

Jóczik

Zimborás

Majoros³

et al. 2022

Applied Sciences

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“…For this reason the use of a monolithic approach for the reduced problem is not a good choice: since the offline solutions are obtained relying on a segregated solver, also at the online level a segregated strategy has to be applied to obtain solutions as consistent as possible. For a discussion on a similar consistent approach in the context of explicit time integration schemes the reader is referred to [43].…”

Section: Proper Orthogonal Decomposition Proceduresmentioning

confidence: 99%

A segregated reduced order model of a pressure-based solver for turbulent compressible flows

Zancanaro¹,

Stabile²,

Rozza³

2022

Preprint

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This article provides a reduced order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of reduced order models capable of providing fully consistent solutions with respect to the high fidelity flow fields. Full order solutions are often obtained through the use of segregated solvers, employing slightly modified conservation laws so that they can be decoupled and then solved one at a time. Classical reduction architectures, on the contrary, rely on the Galerkin projection of a complete Navier-Stokes system to be projected all at once, causing a mild discrepancy with the high order solutions. In this article we rely on segregated reduced order algorithms for the resolution of turbulent and compressible flows in the context of physical and geometrical parameters. At the full order level turbulence is modeled using an eddy viscosity approach. Since there are a variety of different turbulence models for the approximation of this supplementary viscosity, one of the aims of this work is to provide reduced order models which are independent on this selection. This goal is reached by the application of hybrid methods where Navier-Stokes equations are projected in a standard way while the viscosity field is approximated by the use of data-driven interpolation methods or by the evaluation of a properly trained neural network. By exploiting the aforementioned expedients it is possible to reduced the computational cost associated wit fluid flow problems characterized by high Reynolds numbers and elevated Mach numbers.

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“…Specifically, ROM is subdivided into intrusive ROM (IROM) and non-intrusive ROM (NIROM) models. IROM focuses on the projection of full-order governing equations onto low-order spaces in favor of higher solution efficiency (Fang et al, 2014;Galletti et al, 2004;Star et al, 2021;Tello et al, 2020). This approach, as the name indicates, is intrusive to the full-order governing equations as it involves manipulation of the governing equations.…”

Section: Data-driven Modelsmentioning

confidence: 99%

Recent advances in modeling turbulent wind flow at pedestrian-level in the built environment

Zhong

Liu

Zhao

et al. 2022

ARIN

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Pressing problems in urban ventilation and thermal comfort affecting pedestrians related to current urban development and densification are increasingly dealt with from the perspective of climate change adaptation strategies. In recent research efforts, the prime objective is to accurately assess pedestrian-level wind (PLW) environments by using different simulation approaches that have reasonable computational time. This review aims to provide insights into the most recent PLW studies that use both established and data-driven simulation approaches during the last 5 years, covering 215 articles using computational fluid dynamics (CFD) and typical data-driven models. We observe that steady-state Reynolds-averaged Navier-Stokes (SRANS) simulations are still the most dominantly used approach. Due to the model uncertainty embedded in the SRANS approach, a sensitivity test is recommended as a remedial measure for using SRANS. Another noted thriving trend is conducting unsteady-state simulations using high-efficiency methods. Specifically, both the massively parallelized large-eddy simulation (LES) and hybrid LES-RANS offer high computational efficiency and accuracy. While data-driven models are in general believed to be more computationally efficient in predicting PLW dynamics, they in fact still call for substantial computational resources and efforts if the time for development, training and validation of a data-driven model is taken into account. The synthesized understanding of these modeling approaches is expected to facilitate the choosing of proper simulation approaches for PLW environment studies, to ultimately serving urban planning and building designs with respect to pedestrian comfort and urban ventilation assessment.

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Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

Cited by 7 publications

References 85 publications

A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices

A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices

A segregated reduced order model of a pressure-based solver for turbulent compressible flows

Recent advances in modeling turbulent wind flow at pedestrian-level in the built environment

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