Symmetry Reduction and Numerical Solution of Von K a ´ rm a ´ n Swirling Viscous Flow
In this paper, the numerical solutions of von K a ´ rm a ´ n swirling viscous flow are obtained based on the effective combination of the symmetry method and the Runge-Kutta method. Firstly, the multi-parameter symmetry of von K a ´ rm a ´...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-04-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/4/120 |
| _version_ | 1818000294456328192 |
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| author | XiaoMin Wang SuDao Bilige |
| author_facet | XiaoMin Wang SuDao Bilige |
| author_sort | XiaoMin Wang |
| collection | DOAJ |
| description | In this paper, the numerical solutions of von K a ´ rm a ´ n swirling viscous flow are obtained based on the effective combination of the symmetry method and the Runge-Kutta method. Firstly, the multi-parameter symmetry of von K a ´ rm a ´ n swirling viscous flow is determined based on the differential characteristic set algorithm. Secondly, we used the symmetry to reduce von K a ´ rm a ´ n swirling viscous flow to an initial value problem of the original differential equations. Finally, we numerically solve the initial value problem of the original differential equations by using the Runge-Kutta method. |
| first_indexed | 2024-04-14T03:20:09Z |
| format | Article |
| id | doaj.art-82cb39ec221a495b9fa30e9053121173 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T03:20:09Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-82cb39ec221a495b9fa30e90531211732022-12-22T02:15:20ZengMDPI AGSymmetry2073-89942018-04-0110412010.3390/sym10040120sym10040120Symmetry Reduction and Numerical Solution of Von K a ´ rm a ´ n Swirling Viscous FlowXiaoMin Wang0SuDao Bilige1Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, ChinaDepartment of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, ChinaIn this paper, the numerical solutions of von K a ´ rm a ´ n swirling viscous flow are obtained based on the effective combination of the symmetry method and the Runge-Kutta method. Firstly, the multi-parameter symmetry of von K a ´ rm a ´ n swirling viscous flow is determined based on the differential characteristic set algorithm. Secondly, we used the symmetry to reduce von K a ´ rm a ´ n swirling viscous flow to an initial value problem of the original differential equations. Finally, we numerically solve the initial value problem of the original differential equations by using the Runge-Kutta method.http://www.mdpi.com/2073-8994/10/4/120von K a ´ rm a ´ n swirling viscous flowsymmetrydifferential characteristic set algorithmRunge-Kutta method |
| spellingShingle | XiaoMin Wang SuDao Bilige Symmetry Reduction and Numerical Solution of Von K a ´ rm a ´ n Swirling Viscous Flow Symmetry von K a ´ rm a ´ n swirling viscous flow symmetry differential characteristic set algorithm Runge-Kutta method |
| title | Symmetry Reduction and Numerical Solution of Von K
a
´
rm
a
´
n Swirling Viscous Flow |
| title_full | Symmetry Reduction and Numerical Solution of Von K
a
´
rm
a
´
n Swirling Viscous Flow |
| title_fullStr | Symmetry Reduction and Numerical Solution of Von K
a
´
rm
a
´
n Swirling Viscous Flow |
| title_full_unstemmed | Symmetry Reduction and Numerical Solution of Von K
a
´
rm
a
´
n Swirling Viscous Flow |
| title_short | Symmetry Reduction and Numerical Solution of Von K
a
´
rm
a
´
n Swirling Viscous Flow |
| title_sort | symmetry reduction and numerical solution of von k a ´ rm a ´ n swirling viscous flow |
| topic | von K a ´ rm a ´ n swirling viscous flow symmetry differential characteristic set algorithm Runge-Kutta method |
| url | http://www.mdpi.com/2073-8994/10/4/120 |
| work_keys_str_mv | AT xiaominwang symmetryreductionandnumericalsolutionofvonkarmanswirlingviscousflow AT sudaobilige symmetryreductionandnumericalsolutionofvonkarmanswirlingviscousflow |