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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Format: | Article |
Language: | English |
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Peter the Great St.Petersburg Polytechnic University
2023-12-01
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Series: | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
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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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format | Article |
id | doaj.art-30c77a15bd6b4606a250ae07c3b5a164 |
institution | Directory Open Access Journal |
issn | 2405-7223 |
language | English |
last_indexed | 2024-03-08T10:45:06Z |
publishDate | 2023-12-01 |
publisher | Peter the Great St.Petersburg Polytechnic University |
record_format | Article |
series | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
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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