Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis

In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation. Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering 2018-01, Vol.2018 (2018), p.1-8
Main Authors: Wang, Tianlin, Su, Shaojuan, Yu, Peng-Yao, Zhao, Yong
Format: Article
Language:English
Subjects:
Applied mathematics
Computational physics
Decomposition
Engineering
Euler-Lagrange equation
Fluid dynamics
Methods
Neighborhoods
Numerical analysis
Partial differential equations
Quadratures
Rarefaction
Shallow water equations
Shock wave propagation
Shock waves
Shrinkage
Simulation
Turbulence models
Wavelet analysis
Wavelet transforms
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c317t-abebeaedfab0c22de6229c2ea690bc72f6050800f48c2faf7627d8f0a89e6a6b3
container_end_page 8
container_issue 2018
container_start_page 1
container_title Mathematical problems in engineering
container_volume 2018
creator Wang, Tianlin
Su, Shaojuan
Yu, Peng-Yao
Zhao, Yong
description In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation. Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical solution with oscillation. The dual wavelet shrinkage procedure is introduced after applying the local differential quadrature method, which is a straightforward technique to calculate the spatial derivatives. Results free from numerical oscillation can be obtained, which can not only capture the position of shock and rarefaction waves, but also keep the sharp gradient structure within the shock wave. Three model problems—a one-dimensional dam-break flow governed by shallow water equations, and the propagation of a one-dimensional and a two-dimensional shock wave controlled by the Euler equations—are used to confirm the validity of the proposed procedure.
doi_str_mv 10.1155/2018/4859469
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2105000783</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2105000783</sourcerecordid><originalsourceid>FETCH-LOGICAL-c317t-abebeaedfab0c22de6229c2ea690bc72f6050800f48c2faf7627d8f0a89e6a6b3</originalsourceid><addsrcrecordid>eNqF0EFLwzAUwPEiCs7pzbMEPGpdkrZJehxjOmFsBxV3K2n6ohlZ2yWt0m9vZwcePeUdfu8R_kFwTfADIUkyoZiISSySNGbpSTAiCYvChMT8tJ8xjUNCo815cOH9FmNKEiJGwealrWsH3pvyA63aHTijpEVrr4y1sjFViXTl0KoqrSlBOrToanB5ZY1C8337KzzKO_Quv8BCg6altJ03_jI409J6uDq-4-Dtcf46W4TL9dPzbLoMVUR4E8occpBQaJljRWkBjNJUUZAsxbniVDOcYIGxjoWiWmrOKC-ExlKkwCTLo3FwO9ytXbVvwTfZtmpd_wmfUdLvYsxF1Kv7QSlXee9AZ7UzO-m6jODs0C47tMuO7Xp-N_BPUxby2_ynbwYNvQEt_zTFnPfRfwDX63oE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2105000783</pqid></control><display><type>article</type><title>Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis</title><source>ProQuest - Publicly Available Content Database</source><source>Wiley Open Access</source><creator>Wang, Tianlin ; Su, Shaojuan ; Yu, Peng-Yao ; Zhao, Yong</creator><contributor>Markovic, Damijan ; Damijan Markovic</contributor><creatorcontrib>Wang, Tianlin ; Su, Shaojuan ; Yu, Peng-Yao ; Zhao, Yong ; Markovic, Damijan ; Damijan Markovic</creatorcontrib><description>In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation. Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical solution with oscillation. The dual wavelet shrinkage procedure is introduced after applying the local differential quadrature method, which is a straightforward technique to calculate the spatial derivatives. Results free from numerical oscillation can be obtained, which can not only capture the position of shock and rarefaction waves, but also keep the sharp gradient structure within the shock wave. Three model problems—a one-dimensional dam-break flow governed by shallow water equations, and the propagation of a one-dimensional and a two-dimensional shock wave controlled by the Euler equations—are used to confirm the validity of the proposed procedure.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2018/4859469</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Applied mathematics ; Computational physics ; Decomposition ; Engineering ; Euler-Lagrange equation ; Fluid dynamics ; Methods ; Neighborhoods ; Numerical analysis ; Partial differential equations ; Quadratures ; Rarefaction ; Shallow water equations ; Shock wave propagation ; Shock waves ; Shrinkage ; Simulation ; Turbulence models ; Wavelet analysis ; Wavelet transforms</subject><ispartof>Mathematical problems in engineering, 2018-01, Vol.2018 (2018), p.1-8</ispartof><rights>Copyright © 2018 Yong Zhao et al.</rights><rights>Copyright © 2018 Yong Zhao et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c317t-abebeaedfab0c22de6229c2ea690bc72f6050800f48c2faf7627d8f0a89e6a6b3</cites><orcidid>0000-0001-6950-0183</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2105000783/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2105000783?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25753,27924,27925,37012,44590,75126</link.rule.ids></links><search><contributor>Markovic, Damijan</contributor><contributor>Damijan Markovic</contributor><creatorcontrib>Wang, Tianlin</creatorcontrib><creatorcontrib>Su, Shaojuan</creatorcontrib><creatorcontrib>Yu, Peng-Yao</creatorcontrib><creatorcontrib>Zhao, Yong</creatorcontrib><title>Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis</title><title>Mathematical problems in engineering</title><description>In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation. Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical solution with oscillation. The dual wavelet shrinkage procedure is introduced after applying the local differential quadrature method, which is a straightforward technique to calculate the spatial derivatives. Results free from numerical oscillation can be obtained, which can not only capture the position of shock and rarefaction waves, but also keep the sharp gradient structure within the shock wave. Three model problems—a one-dimensional dam-break flow governed by shallow water equations, and the propagation of a one-dimensional and a two-dimensional shock wave controlled by the Euler equations—are used to confirm the validity of the proposed procedure.</description><subject>Applied mathematics</subject><subject>Computational physics</subject><subject>Decomposition</subject><subject>Engineering</subject><subject>Euler-Lagrange equation</subject><subject>Fluid dynamics</subject><subject>Methods</subject><subject>Neighborhoods</subject><subject>Numerical analysis</subject><subject>Partial differential equations</subject><subject>Quadratures</subject><subject>Rarefaction</subject><subject>Shallow water equations</subject><subject>Shock wave propagation</subject><subject>Shock waves</subject><subject>Shrinkage</subject><subject>Simulation</subject><subject>Turbulence models</subject><subject>Wavelet analysis</subject><subject>Wavelet transforms</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqF0EFLwzAUwPEiCs7pzbMEPGpdkrZJehxjOmFsBxV3K2n6ohlZ2yWt0m9vZwcePeUdfu8R_kFwTfADIUkyoZiISSySNGbpSTAiCYvChMT8tJ8xjUNCo815cOH9FmNKEiJGwealrWsH3pvyA63aHTijpEVrr4y1sjFViXTl0KoqrSlBOrToanB5ZY1C8337KzzKO_Quv8BCg6altJ03_jI409J6uDq-4-Dtcf46W4TL9dPzbLoMVUR4E8occpBQaJljRWkBjNJUUZAsxbniVDOcYIGxjoWiWmrOKC-ExlKkwCTLo3FwO9ytXbVvwTfZtmpd_wmfUdLvYsxF1Kv7QSlXee9AZ7UzO-m6jODs0C47tMuO7Xp-N_BPUxby2_ynbwYNvQEt_zTFnPfRfwDX63oE</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>Wang, Tianlin</creator><creator>Su, Shaojuan</creator><creator>Yu, Peng-Yao</creator><creator>Zhao, Yong</creator><general>Hindawi Publishing Corporation</general><general>Hindawi</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0001-6950-0183</orcidid></search><sort><creationdate>20180101</creationdate><title>Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis</title><author>Wang, Tianlin ; Su, Shaojuan ; Yu, Peng-Yao ; Zhao, Yong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c317t-abebeaedfab0c22de6229c2ea690bc72f6050800f48c2faf7627d8f0a89e6a6b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applied mathematics</topic><topic>Computational physics</topic><topic>Decomposition</topic><topic>Engineering</topic><topic>Euler-Lagrange equation</topic><topic>Fluid dynamics</topic><topic>Methods</topic><topic>Neighborhoods</topic><topic>Numerical analysis</topic><topic>Partial differential equations</topic><topic>Quadratures</topic><topic>Rarefaction</topic><topic>Shallow water equations</topic><topic>Shock wave propagation</topic><topic>Shock waves</topic><topic>Shrinkage</topic><topic>Simulation</topic><topic>Turbulence models</topic><topic>Wavelet analysis</topic><topic>Wavelet transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Tianlin</creatorcontrib><creatorcontrib>Su, Shaojuan</creatorcontrib><creatorcontrib>Yu, Peng-Yao</creatorcontrib><creatorcontrib>Zhao, Yong</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East &amp; Africa Database</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer science database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest advanced technologies &amp; aerospace journals</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest - Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Tianlin</au><au>Su, Shaojuan</au><au>Yu, Peng-Yao</au><au>Zhao, Yong</au><au>Markovic, Damijan</au><au>Damijan Markovic</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2018-01-01</date><risdate>2018</risdate><volume>2018</volume><issue>2018</issue><spage>1</spage><epage>8</epage><pages>1-8</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation. Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical solution with oscillation. The dual wavelet shrinkage procedure is introduced after applying the local differential quadrature method, which is a straightforward technique to calculate the spatial derivatives. Results free from numerical oscillation can be obtained, which can not only capture the position of shock and rarefaction waves, but also keep the sharp gradient structure within the shock wave. Three model problems—a one-dimensional dam-break flow governed by shallow water equations, and the propagation of a one-dimensional and a two-dimensional shock wave controlled by the Euler equations—are used to confirm the validity of the proposed procedure.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2018/4859469</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0001-6950-0183</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1024-123X
ispartof Mathematical problems in engineering, 2018-01, Vol.2018 (2018), p.1-8
issn 1024-123X
1563-5147
language eng
recordid cdi_proquest_journals_2105000783
source ProQuest - Publicly Available Content Database; Wiley Open Access
subjects Applied mathematics
Computational physics
Decomposition
Engineering
Euler-Lagrange equation
Fluid dynamics
Methods
Neighborhoods
Numerical analysis
Partial differential equations
Quadratures
Rarefaction
Shallow water equations
Shock wave propagation
Shock waves
Shrinkage
Simulation
Turbulence models
Wavelet analysis
Wavelet transforms
title Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T14%3A12%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Suppressing%20Numerical%20Oscillation%20for%20Nonlinear%20Hyperbolic%20Equations%20by%20Wavelet%20Analysis&rft.jtitle=Mathematical%20problems%20in%20engineering&rft.au=Wang,%20Tianlin&rft.date=2018-01-01&rft.volume=2018&rft.issue=2018&rft.spage=1&rft.epage=8&rft.pages=1-8&rft.issn=1024-123X&rft.eissn=1563-5147&rft_id=info:doi/10.1155/2018/4859469&rft_dat=%3Cproquest_cross%3E2105000783%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c317t-abebeaedfab0c22de6229c2ea690bc72f6050800f48c2faf7627d8f0a89e6a6b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2105000783&rft_id=info:pmid/&rfr_iscdi=true