Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme
Abstract In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonlinear advection–diffusion–dispersion problems. The third-order backward differenti...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02580-6 |
| _version_ | 1818067992689246208 |
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| author | Sunyoung Bu Soyoon Bak |
| author_facet | Sunyoung Bu Soyoon Bak |
| author_sort | Sunyoung Bu |
| collection | DOAJ |
| description | Abstract In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonlinear advection–diffusion–dispersion problems. The third-order backward differentiation formula and fourth-order finite difference schemes are used in temporal and spatial discretizations, respectively. Additionally, to evaluate function values at non-grid points in BSL, the constrained interpolation profile method is used. Several numerical experiments demonstrate the efficiency of the proposed techniques in terms of accuracy and computation costs, compare with existing departure traceback schemes. |
| first_indexed | 2024-12-10T15:32:30Z |
| format | Article |
| id | doaj.art-eb76e9dbe7434d5a8a4784c0d0198f7a |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T15:32:30Z |
| publishDate | 2020-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-eb76e9dbe7434d5a8a4784c0d0198f7a2022-12-22T01:43:20ZengSpringerOpenAdvances in Difference Equations1687-18472020-03-012020111910.1186/s13662-020-02580-6Simulation of advection–diffusion–dispersion equations based on a composite time discretization schemeSunyoung Bu0Soyoon Bak1Department of Liberal Arts, Hongik UniversityDepartment of Mathematics, Kyungpook National UniversityAbstract In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonlinear advection–diffusion–dispersion problems. The third-order backward differentiation formula and fourth-order finite difference schemes are used in temporal and spatial discretizations, respectively. Additionally, to evaluate function values at non-grid points in BSL, the constrained interpolation profile method is used. Several numerical experiments demonstrate the efficiency of the proposed techniques in terms of accuracy and computation costs, compare with existing departure traceback schemes.http://link.springer.com/article/10.1186/s13662-020-02580-6Time-discretization methodSemi-Lagrangian methodAdvection–diffusion equationAdvection–dispersion equationBurgers’ equationsKorteweg-de Vries–Burgers’ equation |
| spellingShingle | Sunyoung Bu Soyoon Bak Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme Advances in Difference Equations Time-discretization method Semi-Lagrangian method Advection–diffusion equation Advection–dispersion equation Burgers’ equations Korteweg-de Vries–Burgers’ equation |
| title | Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme |
| title_full | Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme |
| title_fullStr | Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme |
| title_full_unstemmed | Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme |
| title_short | Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme |
| title_sort | simulation of advection diffusion dispersion equations based on a composite time discretization scheme |
| topic | Time-discretization method Semi-Lagrangian method Advection–diffusion equation Advection–dispersion equation Burgers’ equations Korteweg-de Vries–Burgers’ equation |
| url | http://link.springer.com/article/10.1186/s13662-020-02580-6 |
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