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Runge-Kutta residual distribution schemes

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

Authors

Andrzej Warzynski

MATTHEW HUBBARD MATTHEW.HUBBARD@NOTTINGHAM.AC.UK
Professor of Computational and Applied Mathematics

Mario Ricchiuto



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 http://eprints.nottingham.ac.uk/id/eprint/40821
Publisher URL http://link.springer.com/article/10.1007%2Fs10915-014-9879-0
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9879-0.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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