Runge-Kutta residual distribution schemes

Warzynski, Andrzej; Hubbard, Matthew E.; Ricchiuto, Mario

Abstract

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.

Citation

Warzynski, A., Hubbard, M. E., & Ricchiuto, M. (2015). Runge-Kutta residual distribution schemes. Journal of Scientific Computing, 62(3), https://doi.org/10.1007/s10915-014-9879-0

• Journal Article Type: Article
• Acceptance Date: Jun 4, 2014
• Online Publication Date: Jun 26, 2014
• Publication Date: Mar 31, 2015
• Deposit Date: Feb 27, 2017
• Publicly Available Date: Feb 27, 2017
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Electronic ISSN: 1573-7691
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 62
• Issue: 3
• DOI: https://doi.org/10.1007/s10915-014-9879-0
• Keywords: Hyperbolic conservation laws, Time-dependent problems, Second order schemes, Residual distribution, Runge–Kutta time-stepping
• Public URL: https://nottingham-repository.worktribe.com/output/746355
• Publisher URL: http://link.springer.com/article/10.1007%2Fs10915-014-9879-0
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9879-0.