A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem

In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydr...

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Main Authors: Golubkov Valentin, Garbaruk Andrey
Format: Article
Language:English
Published: Peter the Great St.Petersburg Polytechnic University 2023-12-01
Series:St. Petersburg Polytechnical University Journal: Physics and Mathematics
Subjects:
Online Access:https://physmath.spbstu.ru/article/2023.70.05/
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author Golubkov Valentin
Garbaruk Andrey
author_facet Golubkov Valentin
Garbaruk Andrey
author_sort Golubkov Valentin
collection DOAJ
description In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier–Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on.
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spelling doaj.art-30c77a15bd6b4606a250ae07c3b5a1642024-01-26T17:18:26ZengPeter the Great St.Petersburg Polytechnic UniversitySt. Petersburg Polytechnical University Journal: Physics and Mathematics2405-72232023-12-0116410.18721/JPM.1640520714726A comparison of two approaches to the global stability analysis using the example of the cylinder flow problemGolubkov Valentin0https://orcid.org/0000-0001-9473-7430Garbaruk Andrey1https://orcid.org/0000-0002-2775-9864Peter the Great St. Petersburg Polytechnic UniversityPeter the Great St. Petersburg Polytechnic UniversityIn the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier–Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on.https://physmath.spbstu.ru/article/2023.70.05/global stability analysisnavier–stokes equationsjacobianautomatic differentiation
spellingShingle Golubkov Valentin
Garbaruk Andrey
A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
St. Petersburg Polytechnical University Journal: Physics and Mathematics
global stability analysis
navier–stokes equations
jacobian
automatic differentiation
title A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
title_full A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
title_fullStr A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
title_full_unstemmed A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
title_short A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
title_sort comparison of two approaches to the global stability analysis using the example of the cylinder flow problem
topic global stability analysis
navier–stokes equations
jacobian
automatic differentiation
url https://physmath.spbstu.ru/article/2023.70.05/
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