General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems
The general formulation of the second-order semi-Lagrangian methods was presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include two-step backward difference formula and Crank-Nicolson type semi-Lagrang...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/763630 |
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| _version_ | 1832545656405753856 |
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| author | Xiaohan Long Chuanjun Chen |
| author_facet | Xiaohan Long Chuanjun Chen |
| author_sort | Xiaohan Long |
| collection | DOAJ |
| description | The general formulation of the second-order semi-Lagrangian methods was presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones. And it is easy to be extended to higher-order schemes. We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate. The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed. Finally convergence properties of the semi-Lagrangian finite difference schemes are tested. |
| format | Article |
| id | doaj-art-8d23879d733c4e1a96126f4e0072e741 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8d23879d733c4e1a96126f4e0072e7412025-02-03T07:25:09ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/763630763630General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion ProblemsXiaohan Long0Chuanjun Chen1Department of Mathematics and Information, Ludong University, Yantai 264025, ChinaDepartment of Mathematics and Information Science, Yantai University, Yantai 264005, ChinaThe general formulation of the second-order semi-Lagrangian methods was presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones. And it is easy to be extended to higher-order schemes. We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate. The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed. Finally convergence properties of the semi-Lagrangian finite difference schemes are tested.http://dx.doi.org/10.1155/2013/763630 |
| spellingShingle | Xiaohan Long Chuanjun Chen General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems Abstract and Applied Analysis |
| title | General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems |
| title_full | General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems |
| title_fullStr | General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems |
| title_full_unstemmed | General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems |
| title_short | General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems |
| title_sort | general formulation of second order semi lagrangian methods for convection diffusion problems |
| url | http://dx.doi.org/10.1155/2013/763630 |
| work_keys_str_mv | AT xiaohanlong generalformulationofsecondordersemilagrangianmethodsforconvectiondiffusionproblems AT chuanjunchen generalformulationofsecondordersemilagrangianmethodsforconvectiondiffusionproblems |