A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method
An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/925920 |
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| _version_ | 1832553565994876928 |
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| author | Qiaojie Li Zhoushun Zheng Shuang Wang Jiankang Liu |
| author_facet | Qiaojie Li Zhoushun Zheng Shuang Wang Jiankang Liu |
| author_sort | Qiaojie Li |
| collection | DOAJ |
| description | An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective. |
| format | Article |
| id | doaj-art-b49eb3117aff44be8195eab77544840f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b49eb3117aff44be8195eab77544840f2025-02-03T05:53:42ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/925920925920A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann MethodQiaojie Li0Zhoushun Zheng1Shuang Wang2Jiankang Liu3School of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaAn explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.http://dx.doi.org/10.1155/2012/925920 |
| spellingShingle | Qiaojie Li Zhoushun Zheng Shuang Wang Jiankang Liu A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method Journal of Applied Mathematics |
| title | A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method |
| title_full | A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method |
| title_fullStr | A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method |
| title_full_unstemmed | A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method |
| title_short | A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method |
| title_sort | multilevel finite difference scheme for one dimensional burgers equation derived from the lattice boltzmann method |
| url | http://dx.doi.org/10.1155/2012/925920 |
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