Runge-Kutta residual distribution schemes

Warzynski, Andrzej and Hubbard, Matthew E. and Ricchiuto, Mario (2015) Runge-Kutta residual distribution schemes. Journal of Scientific Computing, 62 (3). pp. 772-802. ISSN 1573-7691

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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.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9879-0.
Keywords: Hyperbolic conservation laws, Time-dependent problems, Second order schemes, Residual distribution, Runge–Kutta time-stepping
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s10915-014-9879-0
Depositing User: Hubbard, Matthew
Date Deposited: 27 Feb 2017 09:53
Last Modified: 28 Feb 2017 01:43
URI: http://eprints.nottingham.ac.uk/id/eprint/40821

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