Third-order modified coefficient scheme based on essentially non-oscillatory scheme
A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process...
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| Veröffentlicht in: | Applied mathematics and mechanics 2008-11, Vol.29 (11), p.1477-1486 |
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| creator | 李明军 杨玉月 舒适 |
| description | A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme. |
| doi_str_mv | 10.1007/s10483-008-1108-x |
| format | Article |
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The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.</description><identifier>ISSN: 0253-4827</identifier><identifier>EISSN: 1573-2754</identifier><identifier>DOI: 10.1007/s10483-008-1108-x</identifier><language>eng</language><publisher>Heidelberg: Shanghai University Press</publisher><subject>Accuracy ; Applications of Mathematics ; Approximation ; Classical Mechanics ; Coefficients ; Construction ; Density ; Fluid- and Aerodynamics ; Mathematical Modeling and Industrial Mathematics ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Preserves ; Tubes ; 力学分析 ; 微分方程 ; 数学模式 ; 普通流体力学</subject><ispartof>Applied mathematics and mechanics, 2008-11, Vol.29 (11), p.1477-1486</ispartof><rights>Shanghai University and Springer-Verlag GmbH 2008</rights><rights>Copyright © Wanfang Data Co. Ltd. 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Math. Mech.-Engl. Ed</addtitle><addtitle>Applied Mathematics and Mechanics(English Edition)</addtitle><description>A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.</description><subject>Accuracy</subject><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Classical Mechanics</subject><subject>Coefficients</subject><subject>Construction</subject><subject>Density</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Preserves</subject><subject>Tubes</subject><subject>力学分析</subject><subject>微分方程</subject><subject>数学模式</subject><subject>普通流体力学</subject><issn>0253-4827</issn><issn>1573-2754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouH78AG_FiyBE89mmRxG_QPDgeg5pOtmNdhNNdnH77410wZuXCUyed2Z4EDqj5IoS0lxnSoTimBCFKS1lu4dmVDYcs0aKfTQjTHIsFGsO0VHO74QQ0QgxQ6_zpU89jqmHVK1i752HvrIRnPPWQ1hX2S5hBVVncvmIoYKcS9ubYRirEAOO2fphMOuYxh17gg6cGTKc7t5j9HZ_N799xM8vD0-3N8_YcsXWmDNgQGpWc2Uk7Zg0veNcCdab1hDROdFK04KsC9b2pHWWUCoVbUzLTOcYP0aX09xvE5wJC_0eNymUjXoc83Y5bDWwIqT4IKrAFxP8meLXBvJar3y2UC4PEDdZKynrpqatLCSdSJtizgmc_kx-ZdKoKdG_svUkW5ex-le23pYMmzK5sGEB6e-W_0Lnu0XLGBZfJac7Yz-cH0AzVTctF5T_AIl3jm4</recordid><startdate>20081101</startdate><enddate>20081101</enddate><creator>李明军 杨玉月 舒适</creator><general>Shanghai University Press</general><general>School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,Hunan Province,P.R.China</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20081101</creationdate><title>Third-order modified coefficient scheme based on essentially non-oscillatory scheme</title><author>李明军 杨玉月 舒适</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-32e2e062638a51b25adf33842da9a04bf495a9e56e2e9d09fc0115817a92abf23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Accuracy</topic><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Classical Mechanics</topic><topic>Coefficients</topic><topic>Construction</topic><topic>Density</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Preserves</topic><topic>Tubes</topic><topic>力学分析</topic><topic>微分方程</topic><topic>数学模式</topic><topic>普通流体力学</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>李明军 杨玉月 舒适</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>李明军 杨玉月 舒适</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Third-order modified coefficient scheme based on essentially non-oscillatory scheme</atitle><jtitle>Applied mathematics and mechanics</jtitle><stitle>Appl. Math. Mech.-Engl. Ed</stitle><addtitle>Applied Mathematics and Mechanics(English Edition)</addtitle><date>2008-11-01</date><risdate>2008</risdate><volume>29</volume><issue>11</issue><spage>1477</spage><epage>1486</epage><pages>1477-1486</pages><issn>0253-4827</issn><eissn>1573-2754</eissn><abstract>A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.</abstract><cop>Heidelberg</cop><pub>Shanghai University Press</pub><doi>10.1007/s10483-008-1108-x</doi><tpages>10</tpages></addata></record> |
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| ispartof | Applied mathematics and mechanics, 2008-11, Vol.29 (11), p.1477-1486 |
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| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Accuracy Applications of Mathematics Approximation Classical Mechanics Coefficients Construction Density Fluid- and Aerodynamics Mathematical Modeling and Industrial Mathematics Mathematical models Mathematics Mathematics and Statistics Partial Differential Equations Preserves Tubes 力学分析 微分方程 数学模式 普通流体力学 |
| title | Third-order modified coefficient scheme based on essentially non-oscillatory scheme |
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