An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems
This paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order c...
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| Veröffentlicht in: | Numerical methods for partial differential equations 2021-05, Vol.37 (3), p.2317-2356 |
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| creator | Liu, Bijin Yu, Ching‐Hao An, Ruidong |
| description | This paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four general weights are determined by applying the Taylor series expansions. (2) These general weights are optimized to the new weights which are derived from the WENO concept and modified wavenumber approach. (3) No dissipation errors are found for the developed OCRWENO‐LD scheme through Fourier analysis. The proposed high‐resolution scheme demonstrates its capability in exhibiting high‐accuracy in smooth regions and avoiding numerical oscillation near discontinuities when simulating the wave equation, Burgers' equation, one‐dimensional Euler equation, porous medium equation, and convection–diffusion Buckley–Leverett equation. |
| doi_str_mv | 10.1002/num.22716 |
| format | Article |
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The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four general weights are determined by applying the Taylor series expansions. (2) These general weights are optimized to the new weights which are derived from the WENO concept and modified wavenumber approach. (3) No dissipation errors are found for the developed OCRWENO‐LD scheme through Fourier analysis. The proposed high‐resolution scheme demonstrates its capability in exhibiting high‐accuracy in smooth regions and avoiding numerical oscillation near discontinuities when simulating the wave equation, Burgers' equation, one‐dimensional Euler equation, porous medium equation, and convection–diffusion Buckley–Leverett equation.</description><identifier>ISSN: 0749-159X</identifier><identifier>EISSN: 1098-2426</identifier><identifier>DOI: 10.1002/num.22716</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley & Sons, Inc</publisher><subject>Advection ; Burgers equation ; compact stencils ; dissipation errors ; Essentially non-oscillatory schemes ; Euler-Lagrange equation ; Fourier analysis ; high‐resolution ; non‐oscillation ; Porous media ; Reconstruction ; Series expansion ; Taylor series ; Wave equations ; Wavelengths</subject><ispartof>Numerical methods for partial differential equations, 2021-05, Vol.37 (3), p.2317-2356</ispartof><rights>2020 Wiley Periodicals LLC</rights><rights>2021 Wiley Periodicals LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2576-c2c2f8111b013d62f88e986d7138bcf3f30f74d4c4ae6d89bd8521fd41d27f083</cites><orcidid>0000-0002-9895-2418</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnum.22716$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnum.22716$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27903,27904,45553,45554</link.rule.ids></links><search><creatorcontrib>Liu, Bijin</creatorcontrib><creatorcontrib>Yu, Ching‐Hao</creatorcontrib><creatorcontrib>An, Ruidong</creatorcontrib><title>An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems</title><title>Numerical methods for partial differential equations</title><description>This paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four general weights are determined by applying the Taylor series expansions. (2) These general weights are optimized to the new weights which are derived from the WENO concept and modified wavenumber approach. (3) No dissipation errors are found for the developed OCRWENO‐LD scheme through Fourier analysis. The proposed high‐resolution scheme demonstrates its capability in exhibiting high‐accuracy in smooth regions and avoiding numerical oscillation near discontinuities when simulating the wave equation, Burgers' equation, one‐dimensional Euler equation, porous medium equation, and convection–diffusion Buckley–Leverett equation.</description><subject>Advection</subject><subject>Burgers equation</subject><subject>compact stencils</subject><subject>dissipation errors</subject><subject>Essentially non-oscillatory schemes</subject><subject>Euler-Lagrange equation</subject><subject>Fourier analysis</subject><subject>high‐resolution</subject><subject>non‐oscillation</subject><subject>Porous media</subject><subject>Reconstruction</subject><subject>Series expansion</subject><subject>Taylor series</subject><subject>Wave equations</subject><subject>Wavelengths</subject><issn>0749-159X</issn><issn>1098-2426</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEqWw4A8ssWLR1uO8nGVV8ZIKbKjEzkr8oK6SONgOVVjxCXwjX0IgbNnMjHTPnStdhM6BzIEQumi6ek5pBukBmgDJ2YzGND1EE5LF-QyS_PkYnXi_IwQggXyCtssG2zaY2rwriYWt20IE7JSwjQ-uE8HYBu-VedmGQVfeqyaYoqp63Njm6-PTemGqqgjW9diLraoV1tbhQr6p0ds6W1aq9qfoSBeVV2d_e4o211dPq9vZ-vHmbrVczwRNsnSYgmoGACWBSKbDzVTOUplBxEqhIx0RncUyFnGhUsnyUrKEgpYxSJppwqIpuhj_DsGvnfKB72znmiGS04TklEGawkBdjpRw1nunNG-dqQvXcyD8p0g-FMl_ixzYxcjuTaX6_0H-sLkfHd8OyHhY</recordid><startdate>202105</startdate><enddate>202105</enddate><creator>Liu, Bijin</creator><creator>Yu, Ching‐Hao</creator><creator>An, Ruidong</creator><general>John Wiley & Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-9895-2418</orcidid></search><sort><creationdate>202105</creationdate><title>An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems</title><author>Liu, Bijin ; Yu, Ching‐Hao ; An, Ruidong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2576-c2c2f8111b013d62f88e986d7138bcf3f30f74d4c4ae6d89bd8521fd41d27f083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Advection</topic><topic>Burgers equation</topic><topic>compact stencils</topic><topic>dissipation errors</topic><topic>Essentially non-oscillatory schemes</topic><topic>Euler-Lagrange equation</topic><topic>Fourier analysis</topic><topic>high‐resolution</topic><topic>non‐oscillation</topic><topic>Porous media</topic><topic>Reconstruction</topic><topic>Series expansion</topic><topic>Taylor series</topic><topic>Wave equations</topic><topic>Wavelengths</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Bijin</creatorcontrib><creatorcontrib>Yu, Ching‐Hao</creatorcontrib><creatorcontrib>An, Ruidong</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Numerical methods for partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Bijin</au><au>Yu, Ching‐Hao</au><au>An, Ruidong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems</atitle><jtitle>Numerical methods for partial differential equations</jtitle><date>2021-05</date><risdate>2021</risdate><volume>37</volume><issue>3</issue><spage>2317</spage><epage>2356</epage><pages>2317-2356</pages><issn>0749-159X</issn><eissn>1098-2426</eissn><abstract>This paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four general weights are determined by applying the Taylor series expansions. (2) These general weights are optimized to the new weights which are derived from the WENO concept and modified wavenumber approach. (3) No dissipation errors are found for the developed OCRWENO‐LD scheme through Fourier analysis. The proposed high‐resolution scheme demonstrates its capability in exhibiting high‐accuracy in smooth regions and avoiding numerical oscillation near discontinuities when simulating the wave equation, Burgers' equation, one‐dimensional Euler equation, porous medium equation, and convection–diffusion Buckley–Leverett equation.</abstract><cop>Hoboken, USA</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/num.22716</doi><tpages>79</tpages><orcidid>https://orcid.org/0000-0002-9895-2418</orcidid></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Advection Burgers equation compact stencils dissipation errors Essentially non-oscillatory schemes Euler-Lagrange equation Fourier analysis high‐resolution non‐oscillation Porous media Reconstruction Series expansion Taylor series Wave equations Wavelengths |
| title | An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems |
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