Runge-Kutta residual distribution schemes
We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type time-stepping (discretisation in time). The introd...
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| Format: | Article |
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Springer
2015
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| Online Access: | https://eprints.nottingham.ac.uk/40821/ |
| _version_ | 1848796140621791232 |
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| author | Warzynski, Andrzej Hubbard, Matthew E. Ricchiuto, Mario |
| author_facet | Warzynski, Andrzej Hubbard, Matthew E. Ricchiuto, Mario |
| author_sort | Warzynski, Andrzej |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type time-stepping (discretisation in time). The introduced non-linear blending procedure allows us to retain the explicit character of the time-stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given. |
| first_indexed | 2025-11-14T19:43:15Z |
| format | Article |
| id | nottingham-40821 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:15Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-408212020-05-04T17:03:41Z https://eprints.nottingham.ac.uk/40821/ Runge-Kutta residual distribution schemes Warzynski, Andrzej Hubbard, Matthew E. Ricchiuto, Mario We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type time-stepping (discretisation in time). The introduced non-linear blending procedure allows us to retain the explicit character of the time-stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given. Springer 2015-03-31 Article PeerReviewed Warzynski, Andrzej, Hubbard, Matthew E. and Ricchiuto, Mario (2015) Runge-Kutta residual distribution schemes. Journal of Scientific Computing, 62 (3). pp. 772-802. ISSN 1573-7691 Hyperbolic conservation laws Time-dependent problems Second order schemes Residual distribution Runge–Kutta time-stepping http://link.springer.com/article/10.1007%2Fs10915-014-9879-0 doi:10.1007/s10915-014-9879-0 doi:10.1007/s10915-014-9879-0 |
| spellingShingle | Hyperbolic conservation laws Time-dependent problems Second order schemes Residual distribution Runge–Kutta time-stepping Warzynski, Andrzej Hubbard, Matthew E. Ricchiuto, Mario Runge-Kutta residual distribution schemes |
| title | Runge-Kutta residual distribution schemes |
| title_full | Runge-Kutta residual distribution schemes |
| title_fullStr | Runge-Kutta residual distribution schemes |
| title_full_unstemmed | Runge-Kutta residual distribution schemes |
| title_short | Runge-Kutta residual distribution schemes |
| title_sort | runge-kutta residual distribution schemes |
| topic | Hyperbolic conservation laws Time-dependent problems Second order schemes Residual distribution Runge–Kutta time-stepping |
| url | https://eprints.nottingham.ac.uk/40821/ https://eprints.nottingham.ac.uk/40821/ https://eprints.nottingham.ac.uk/40821/ |