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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.

Journal Article Type Article
Publication Date Mar 31, 2015
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 1573-7691
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 62
Issue 3
APA6 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
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
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.nottingh.../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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