Stability evaluation of approximate Riemann solvers using the direct Lyapunov method

Stability evaluation of approximate Riemann solvers using the direct Lyapunov method

The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the approximate Riemann solvers. The pressure perturbation feedin...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Gogoi, Aishwarjya, Mandal, Jadav Chandra, Saraf, Amitabh
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Gogoi, Aishwarjya
Mandal, Jadav Chandra
Saraf, Amitabh
description The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities are found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers.
doi_str_mv 10.48550/arxiv.2403.17504
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2403_17504</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2403_17504</sourcerecordid><originalsourceid>FETCH-LOGICAL-a674-20e0dabcef49ccd8739a68a285f26ca86b4077b2cc7d72c5b4f672da40b2cb4e3</originalsourceid><addsrcrecordid>eNotz01qwzAUBGBtuihpD9BVdQG7iixbyjKE_oGhkHpvnqSnRGBbRpZNfPumaVcDsxjmI-Rpy3KhypK9QLz4JeeCFflWlkzck-Y7gfadTyvFBboZkg8DDY7COMZw8T0kpEePPQwDnUK3YJzoPPnhRNMZqfURTaL1CuM8hIX2mM7BPpA7B92Ej_-5Ic3ba3P4yOqv98_Dvs6gkiLjDJkFbdCJnTFWyWIHlQKuSscrA6rSgkmpuTHSSm5KLVwluQXBrp0WWGzI89_sjdWO8fo2ru0vr73xih-taUz_</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Stability evaluation of approximate Riemann solvers using the direct Lyapunov method</title><source>arXiv.org</source><creator>Gogoi, Aishwarjya ; Mandal, Jadav Chandra ; Saraf, Amitabh</creator><creatorcontrib>Gogoi, Aishwarjya ; Mandal, Jadav Chandra ; Saraf, Amitabh</creatorcontrib><description>The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities are found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers.</description><identifier>DOI: 10.48550/arxiv.2403.17504</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2024-03</creationdate><rights>http://creativecommons.org/licenses/by-nc-nd/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2403.17504$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2403.17504$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Gogoi, Aishwarjya</creatorcontrib><creatorcontrib>Mandal, Jadav Chandra</creatorcontrib><creatorcontrib>Saraf, Amitabh</creatorcontrib><title>Stability evaluation of approximate Riemann solvers using the direct Lyapunov method</title><description>The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities are found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz01qwzAUBGBtuihpD9BVdQG7iixbyjKE_oGhkHpvnqSnRGBbRpZNfPumaVcDsxjmI-Rpy3KhypK9QLz4JeeCFflWlkzck-Y7gfadTyvFBboZkg8DDY7COMZw8T0kpEePPQwDnUK3YJzoPPnhRNMZqfURTaL1CuM8hIX2mM7BPpA7B92Ej_-5Ic3ba3P4yOqv98_Dvs6gkiLjDJkFbdCJnTFWyWIHlQKuSscrA6rSgkmpuTHSSm5KLVwluQXBrp0WWGzI89_sjdWO8fo2ru0vr73xih-taUz_</recordid><startdate>20240326</startdate><enddate>20240326</enddate><creator>Gogoi, Aishwarjya</creator><creator>Mandal, Jadav Chandra</creator><creator>Saraf, Amitabh</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240326</creationdate><title>Stability evaluation of approximate Riemann solvers using the direct Lyapunov method</title><author>Gogoi, Aishwarjya ; Mandal, Jadav Chandra ; Saraf, Amitabh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-20e0dabcef49ccd8739a68a285f26ca86b4077b2cc7d72c5b4f672da40b2cb4e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Gogoi, Aishwarjya</creatorcontrib><creatorcontrib>Mandal, Jadav Chandra</creatorcontrib><creatorcontrib>Saraf, Amitabh</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Gogoi, Aishwarjya</au><au>Mandal, Jadav Chandra</au><au>Saraf, Amitabh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability evaluation of approximate Riemann solvers using the direct Lyapunov method</atitle><date>2024-03-26</date><risdate>2024</risdate><abstract>The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities are found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers.</abstract><doi>10.48550/arxiv.2403.17504</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2403.17504
ispartof
issn
language eng
recordid cdi_arxiv_primary_2403_17504
source arXiv.org
subjects Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
title Stability evaluation of approximate Riemann solvers using the direct Lyapunov method
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-11T13%3A11%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stability%20evaluation%20of%20approximate%20Riemann%20solvers%20using%20the%20direct%20Lyapunov%20method&rft.au=Gogoi,%20Aishwarjya&rft.date=2024-03-26&rft_id=info:doi/10.48550/arxiv.2403.17504&rft_dat=%3Carxiv_GOX%3E2403_17504%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true