A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries
A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D c...
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| Format: | Article |
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Elsevier
2014
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| Online Access: | https://eprints.nottingham.ac.uk/40810/ |
| _version_ | 1848796138751131648 |
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| author | Morales-Hernandez, Mario Hubbard, Matthew E. Garcia-Navarro, Pilar |
| author_facet | Morales-Hernandez, Mario Hubbard, Matthew E. Garcia-Navarro, Pilar |
| author_sort | Morales-Hernandez, Mario |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D case related to source terms, boundary conditions and the reduction of the time step in the presence of large discontinuities. The boundary conditions treatment as well as the wet/dry fronts in the case of the 2D shallow water equations require extra effort. The proposed scheme is tested on linear and non-linear equations and systems, with and without source terms. The numerical results are compared with those of the conventional scheme as well as with analytical solutions and experimental data. |
| first_indexed | 2025-11-14T19:43:13Z |
| format | Article |
| id | nottingham-40810 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:13Z |
| publishDate | 2014 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-408102020-05-04T16:46:39Z https://eprints.nottingham.ac.uk/40810/ A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries Morales-Hernandez, Mario Hubbard, Matthew E. Garcia-Navarro, Pilar A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D case related to source terms, boundary conditions and the reduction of the time step in the presence of large discontinuities. The boundary conditions treatment as well as the wet/dry fronts in the case of the 2D shallow water equations require extra effort. The proposed scheme is tested on linear and non-linear equations and systems, with and without source terms. The numerical results are compared with those of the conventional scheme as well as with analytical solutions and experimental data. Elsevier 2014-04-15 Article PeerReviewed Morales-Hernandez, Mario, Hubbard, Matthew E. and Garcia-Navarro, Pilar (2014) A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries. Journal of Computational Physics, 263 . pp. 303-327. ISSN 0021-9991 Large time step scheme; Wet/dry fronts; Source terms; Dimensional splitting; 2D shallow water flows http://www.sciencedirect.com/science/article/pii/S0021999114000461 doi:10.1016/j.jcp.2014.01.019 doi:10.1016/j.jcp.2014.01.019 |
| spellingShingle | Large time step scheme; Wet/dry fronts; Source terms; Dimensional splitting; 2D shallow water flows Morales-Hernandez, Mario Hubbard, Matthew E. Garcia-Navarro, Pilar A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries |
| title | A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries |
| title_full | A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries |
| title_fullStr | A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries |
| title_full_unstemmed | A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries |
| title_short | A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries |
| title_sort | 2d extension of a large time step explicit scheme (cfl>1) for unsteady problems with wet/dry boundaries |
| topic | Large time step scheme; Wet/dry fronts; Source terms; Dimensional splitting; 2D shallow water flows |
| url | https://eprints.nottingham.ac.uk/40810/ https://eprints.nottingham.ac.uk/40810/ https://eprints.nottingham.ac.uk/40810/ |